For 45 years it has lain abandoned in David Hockney’s Los Angeles home, an artistic reject that caused a temporary breakdown in relations between the painter and his parents. Now, for the first time since its creation in 1975, a portrait by Hockney of his mother and father will be seen publicly as part of an exhibition opening this week at the National Portrait Gallery.

My Parents and Myself – the painting shows the artist’s face reflected in a mirror between his father and mother – was a source of frustration to Hockney, who eventually gave up on it. But a later version, completed in 1977 and entitled just My Parents, drew on a couple of originals to become one of his most famous works.

“They were both started when I was in Paris,” said Hockney, of My Parents and Myself and another, even earlier version, which had a red triangle in the background. “I later destroyed the one with the triangle. Too contrived.” He persevered with the next version, before giving that up too. “I wasn’t going to destroy it all these years later. It was, after all, painted from life. And my parents aren’t here now.”

His decision to scrap the painting led to a brief rift between Hockney and his father, Kenneth. “Mum and Dad had been to Paris a couple of times to sit,” said the artist’s sister, Margaret. “David even sketched Dad when he was a patient in hospital in the UK. David got them to sit for him again when he moved back to London; they would be a difficult subject matter, I’m sure. So I wasn’t surprised when Mum told me in August 1976 that David had called to say he’d decided to abandon his portrait of them. Mum was naturally upset but had to respect David’s decision.” Her mother’s diary stated: “David has decided to scrap his painting of Ken and I. Much depressed yesterday, but feel better now after his decision.”

David has decided to scrap his painting of Ken and I. Much depressed yesterday, but feel better now after his decision Laura Hockney

Kenneth’s anger, however, was more palpable. “Dad was furious and phoned David to tell him so. A short time later, Dad repented, and phoned David again. He told him: ‘David, disregard what I have said. I’m sorry.’”

Today, Hockney is circumspect over why he did not like My Parents and Myself. “There were too many visitors coming to Paris to see me,” he said. However, Sarah Howgate, curator of the new exhibition, has her own theories. “He overworked the painting. Painted it too much. His father is also too stiff,” she said.

After leaving Paris, Hockney returned to his rented house in Notting Hill. “I got peace and quiet there, and eventually did another version in 1977.” This is the now celebrated My Parents, which left out the mirror image of the artist and which has been owned by Tate Britain for many years. Hockney’s retrospective there in 2017 drew its highest ever number of paying visitors.

For his reworked portrait, Hockney painted his father leaning over to read a book. On the bottom shelf of a dresser, placed between his parents, are six volumes of Marcel Proust’s À la Recherche du Temps Perdu. “His father is in a more natural pose,” said Howgate. Hockney’s mother, Laura, noted with pleasure in her diary that her son had returned to the project: “He’s started again on portrait. I ask what changed his mind. What influence? He says he has a new inspiration. I only want him to be happy and satisfied with his work. Nothing less will do!”

Hockney’s revised version of the portrait, the now-celebrated My Parents (1977). Photograph: David Hockney/Tate London

My Parents was displayed at London’s Hayward Gallery in July 1977. “Mum and Dad were very proud of it, and felt all the sittings had been worthwhile,” said Margaret Hockney. They attended the unveiling, being photographed standing either side of the portrait, while David sat in front.

“Mum and Dad loved seeing the media reports, and Dad bought several copies of the newspapers – in case one got ruined, I suppose.”

Kenneth Hockney, a clerk from Bradford, died in 1978, while Laura, a subject of many paintings and drawings by her son, died in 1999 at 98.

My Parents and Myself, which still has three pieces of masking tape on the canvas, will be displayed just outside the main NPG exhibition as the show itself, David Hockney: Drawing From Life, is of drawings from the past five decades of a small group of his regular sitters. These include his mother; his “muse” Celia Birtwell, the designer who was in Hockney’s famous portrait Mr and Mrs Clark and Percy; and friends Gregory Evans and Maurice Payne. A handful have not been displayed before. There are also previously unseen studies of his A Rake’s Progress, based on his hedonistic first trip to California in 1961.

Running parallel with the NPG exhibition will be a show at Annely Juda gallery, off Bond Street, of Hockney’s recent charcoal and crayon drawings – mainly of friends, plus one of Ed Sheeran from August 2018.