Back when peace did not seem such an impossibility, it was fashionable to cast the Middle East conflict as a family feud. Jews and Arabs were held to be if not brothers then long-lost cousins – the descendants, of Isaac and Ishmael, perhaps, or of Jacob and Esau – who would one day end their estrangement in an embrace. After the collapse of the Oslo peace process, a second intifada and a lethal military offensive in Gaza, you don't hear that kind of talk so much these days.

Yet for at least one family that fanciful, even romantic, notion is a long-buried and painful reality. A new film, receiving its UK debut next week at the UK Jewish film festival, tells the true and astonishing story of a single family divided both by the kind of heartbreak that can split any family anywhere and by what is commonly regarded as the world's most bitter and intractable conflict.

Blood Relation comes from Noa Ben-Hagai, a young Israeli documentary maker, who four years ago made a jaw-dropping discovery – a stash of letters and photographs hidden away by her late grandmother. They revealed what no one had ever told Noa: her grandmother had had a sister, Pnina, who, in circumstances hazy with mystery, had ended up "living as an Arab" in a Palestinian refugee camp in the city of Nablus. Pnina was a Jew but her husband was a Palestinian Arab, as were her eight children and their children. Noa suddenly discovered not only a great-aunt she had never heard of but also a large extended family on the other side of the national divide – among the enemy.

"It was hidden behind a high wall of silence," Noa says, recalling the determination with which her grandmother Rachel – who died when Noa was 15 – had kept her sister a secret. Rachel had held on to the "letters of abandonment" her sister Pnina had written to her, but she had rarely replied.

The film seeks to uncover what happened to Pnina, how a Jewish girl ended up removed from her brothers and sisters, on the other side of the Israeli-Palestinian battle-line. It also lays bare what happens when the two sides of this torn family encounter each other today, revealing the guilt, resentment and stubborn sense of kinship that has not faded in 70 years.

Both these stories, past and present, are compelling as family dramas, the kind of tales packed with secrets and lies that lurk in so many families. But they also serve as a poignant parable for the wider Middle East conflict, highlighting the many ways in which, after all, the war of Arabs and Israelis resembles a family affair.

In seeking to get to the bottom of Pnina's fate, Noa discovers what anyone digging deep into their family history soon learns: myths abound. Truths are handed down that are not truths, exaggerations harden into legends. So Noa's Israeli relatives tell her that in 1940, Pnina, then 14, was kidnapped, perhaps while hitching a ride away from the family homestead in the poor Galilee farming village of Yavniel. She was snatched, they say, by an Arab man who promptly took her to his home in Jaffa. She was not heard from again for nearly 27 years. During the 1948 war that attended Israel's birth, the Arabs of Jaffa – now including the Jewish-born Pnina – had fled to the West Bank, where they lived, following the 1967 war, under Israeli occupation. Why did she never come back to Israel? They asked her to, but she refused.

That's the version told by the Israeli relatives, including an elderly sister who admits Pnina "never said [a man] kidnapped her – but we know he did".

From Pnina's daughters, Noa hears a different story. The way they heard it, Pnina was raised in a rich Jewish family with an Arab maid. The young Pnina would watch the pious Muslim girl saying her prayers, and was one day so moved she asked if they could pray together. Later, the maid's father gave Pnina a lift back to their village, where she completed her spiritual journey by converting to Islam. Why did she never go back to Israel? Because her previous family refused to take her back.

The gulf between the two accounts will be recognised by anyone familiar with ancient but bitter family rows, in which the two warring sides can't even agree on the basic facts. It also echoes the so-called war of narratives, in which Israelis and Palestinians have radically different perspectives on the past that preceded their present dispute. In this, the two sides of Noa's unique family – with their incompatible versions of history – are utterly true to their national roles.

Eventually, through doggedly tracking down anyone with memories from the small village where Rachel and Pnina were raised, Noa assembled an account she could hold on to. She agrees that the year of her great-aunt's departure was 1940 and that it happened when – in a widely forgotten episode – Mussolini's fighter planes strafed the northern city of Haifa in what was then Palestine. But "I don't believe Arabs kidnapped her, nor that she fell in love," says Noa.

She thinks the heart of the matter was scandal: Pnina was pregnant. Noa interviewed an elderly villager who brutally declares that the teenage girl was notoriously loose. No beauty, she would do it "for candy", he says – "Anyone could have her."

Unable to deal with the shame, her family recoiled until Pnina ran away. She was taken in by an Arab man who, says Noa, "rescued her?…?accepted her", despite the fact she was carrying another man's child. To her family, the fact she had gone with an Arab compounded the disgrace; after that, they shunned her.

Pnina lived in fear of her father, afraid he would kill her for the double shame she had inflicted on the family. When her sister later told her to come home – to what was now Israel – Pnina refused, knowing that Arab tradition would oblige her to leave her children behind. Rachel warned her then that if she didn't come, all ties would be severed: she would be dead to them. So began the long silence broken only by Pnina's letters, ever more plaintive pleas to her siblings to visit her in the refugee camp, not to forget her – texts aching with longing and melancholy that continued to arrive until Pnina's death in 1971. "Every day I ask, when will you come? I miss you every day. You are my family."

Noa's research took her to the West Bank, to meet Pnina's children and grandchildren. Most did not want to talk, anxious that any contact with an Israeli – let alone an admission of Jewish ancestry – would raise suspicions of collaboration among their fellow Palestinians. The only one of Pnina's eight children who agreed to speak to her was Salma, a middle-aged woman who had reached rock bottom: "She had no money, she had no work, she needed money for food – she had nothing to lose." With a husband and sons in and out of Israeli custody, usually for trying to work in Israel without a permit, Salma reckoned that contact with an Israeli might prove helpful – especially as Noa's uncle, Shmulik, is a former military governor of Ramallah, in charge for a time of military intelligence on the West Bank. Salma was keen to make contact, sensing that her Israeli cousins might be a lifeline.

The Israelis are not so sure. Noa's camera records her mother, uncles and others debating the wisdom of the family reunion Noa is planning. "What will we gain from this, except helping them out?" asks Shmulik's wife, Sarah. Great-uncle David is worried that, if they help Salma, 10 more Palestinian relatives will pop up demanding similar assistance: "That's our problem with the refugees. They left with two or three children, now they're clans!" In that sentence he speaks for those many Israelis who believe that, while the estimated 700,000 refugees of 1948 might be eligible for some kind of restitution, it's too much to compensate the many millions who now make up the Palestinian nation.

The encounter in the film is tense, confusing and touching all at the same time. Simultaneously you're watching a meeting of Israeli and Palestinian strangers – always awkward – and the reuniting of a family. You ask yourself a basic but profound question: are these people – so divided that on one side stands a retired Israeli military governor and on the other young Palestinian men who include some linked to terrorist organisations – a family or not? "If you look closely," says Noa, "you can see they are the same. They look the same, they speak the same language." And yet they are worlds apart.

The key tension arises between Salma and Shmulik. She needs his money and believes that, as they share the same blood, he should give it. He is torn: one moment he loudly resents her demands, the next he is phoning old contacts and paying bail in order to get Salma's husband out of jail.

Partly this is an age-old family story: the rich man who believes his poor relations are sponging off him, the poor relative who resents her cousin's wealth, the guilt and obligations that come with blood ties. But there is also an echo of the wider story, starting with the perennial Israeli fear that, if you grant one concession, the Palestinians will come back wanting more.

One of the most powerful moments in Noa's journey came when she gathered her Israeli relatives together to debate what they should do about their newly discovered cousins. "Are we ready to accept them as our family?" someone asked. The debate reached a kind of climax when an uncle stated plainly, as if making a confession: "I have a cousin called Salma." At issue here is the question that may well be at the heart of the Israeli-Palestinian dispute: recognition.

Noa found that her sessions with Salma and another daughter of Pnina's became especially intense because the two women seized on the film-maker as a connection with, and a reminder of, their late mother. "All they want is to be accepted by the family. They got it from her, this longingness: they want to be accepted by us as equal human beings." What they want is recognition.

The story of Pnina, Salma, Shmulik and Noa provides countless such insights into the conflict in which they are all tangled up. We see that fear lives even among the strong: when Shmulik visits Salma at her home, driving alone in the West Bank, he calls for directions, admitting he's scared. As governor of Ramallah, he made no contact with his cousins, fearing that if his military superiors knew there were Arabs in his family, his career prospects would be harmed.

We see, too, the strange connections that tie these enemies close together. Fascinatingly, Pnina's family were not Jewish immigrants to Palestine caught up in the early waves of Zionist settlement: they had roots in the country going back generations. They came originally from Tiberias, a mixed city of Jews and Arabs, speaking Arabic at home. Precisely described, they were Palestinian Jews. Yet far from that engendering a sense of kinship or solidarity with the Palestinian Arabs, it has, Noa believes, produced the opposite sentiment. Arabs, one interviewee told her, were associated with "poverty, neglect, primitiveness". Noa's grandmother, the rest of her siblings and her children were keen to see themselves as modern Israelis, not to be reminded of their proximity to the Palestinian "natives". Pnina's marriage to an Arab – in contrast with Noa's mother and her uncle Shmulik, who both married Ashkenazi, or European Jewish, partners – seemed an unforgivable step backward. "Our family was once like the Arabs of Israel," says Noa. "But all this time they ran away from this legacy." When they see Salma and her children, "it's like looking in the mirror; it's very frightening".

By the end of Blood Relation, there is no emotional breakthrough, no sudden comprehension of all these complex feelings. Shmulik struggles to relate to his Palestinian cousins in anything but the old way he learned during military service: he speaks to Salma in a kind of interrogator's Arabic. At one point, he suggests that a possible solution to Salma's economic woes would be for him to hire her as his cook and cleaner. When Noa says a real family relationship is impossible because of the occupation, Shmulik is indignant: "What's the occupation got to do with it?"

Noa's investigation has provided no catharsis: her family accuses her of opening a sore better left untouched. And she has not brought the Middle East conflict to a symbolic end with a Jacob-and-Esau-style embrace of long-lost brothers. Instead, she has revealed feelings that run through so many families, even those not rendered extraordinary by a long-running war. Pnina's yearning is exquisite and explicit in those repeated letters. But her younger, Israeli brother, David, outwardly so tough, expresses similar pain when he recalls the first time he saw Pnina in Nablus: "I found a sister who was a complete stranger to me."