It’s the night after the Baftas and Rebecca Miller has the tired but jaunty air of a woman whose husband has just won a really big award. In a sort of dynastic double whammy, Miller, the daughter of Arthur Miller, the late American playwright and Pulitzer laureate, is married to Daniel Day-Lewis, the Oscar-winning actor and son of Cecil Day-Lewis who was, among other things, our own poet laureate. It’s Laureate City, with a bit of Old Hollywood thrown in (Miller père was married, inter alia, to Marilyn Monroe).

Prior to meeting her I have formed the impression that she is going to be earnest and slightly uptight and that talking about anything may be a bit like pulling teeth. But then I read her forthcoming novel, The Private Lives of Pippa Lee, and it is so good that I get sidetracked from the Arthur-Marilyn-Daniel Day-Lewis malarkey and she ends up being very good value – and heartily relieved that we’ve talked about things other than her family (“Oh God, if you didn’t mention that stuff it would just be so cool – it would be the coolest thing in the world. It’s never happened yet”).

Also, since her book is about the struggle that wives have trying to retain their own identity and not be subsumed into their husband’s, it’s all pretty relevant.

Rebecca is Miller’s daughter with his third wife Inge Morath, a successful Magnum photographer who met Miller when she went to take Monroe’s picture – Monroe being Miller’s wife at the time. The couple were married in 1962 and remained together until Morath’s death in 2002. Morath and Miller also had a son, Daniel, who has Down’s syndrome and who Miller insisted be sent to a “home” from infancy, reportedly because he did not want Rebecca to grow up with “a mongoloid”. Daniel’s mother visited him regularly, his father did not.

According to reports, it was Day-Lewis, by now married to Rebecca, who agitated for a rapprochement between father and son in the late 1990s. Rebecca has said that Daniel, now 41, is “very much a part of our family” and “leads a very active, happy life surrounded by people who love him”.

Rebecca’s childhood had elements of normalcy – Miller and Morath were not especially glitzy – as well as elements of haute bohemia: from birth to the age of six, she lived with her parents in suite 614 of the legendary Chel-sea hotel in New York, which Norman Mailer, Lou Reed and Bob Dylan also called home.

After that the family moved to a farm in Con-necticut, where they remained and where Miller breathed his last in 2005, aged 89, surrounded by family.

Miller, it turns out, discusses the inner lives of women with an insight and acuity that belie her glamorous bohemian roots. Also, she is not earnest at all: she’s clever and smiley and wryly funny. “No, I’m not earnest,” she laughs. “I’m the opposite of earnest. But people always expect me to be. Maybe it’s my face – when I was a kid, I learnt that moody girls got all the attention. It wasn’t cool to be cheerful. I had to learn how to be in a bad mood.”

Face aside, this may also relate to the fact that she is clearly not entirely comfortable with the dynastic aspects of her life, or with smiling on the red carpet on the arm of Day-Lewis. At the Baftas she posed dutifully enough but with a resigned sort of expression and smiled a slightly tight smile when her husband, in his acceptance speech for his best actor award for There Will Be Blood, thanked “Sergeant-Major Miller” and the TV cameras panned to her. You would think she would be used to the glare of the flashlight – having a photographer for a mother – but to say she doesn’t seem mad keen on it would be something of an understatement.

Anyway, here she is, curled up on the sofa, long-limbed and fresh-faced – she looks like she lives in rural Ireland (which she does, in Co Wicklow) via Notting Hill. She is friendly and open and quick to laugh, but there is an element of vulnerability about her, or perhaps it’s wariness. But she is obviously pleased when I tell her how much I like her novel.

This is her first, although she has previously written a well received book of short stories. She is also a film maker and is turning her novel into a film that will star Julianne Moore, Winona Ryder and Robin Wright Penn.

The Private Lives of Pippa Lee is about an American power couple – Mr Lee is a grand publisher and his wife is, well, “just” his wife, fragrant and devoted. She is also unravelling. The book is set in an old people’s gated housing community called Marigold Village, which the couple have just moved to. Pippa is 50 and her husband a feisty but fading 80.

Pippa is a perfect artist’s wife (and after all that is something Rebecca should know about), “placing, giving, intelligent, beautiful, great cook”. But, being a woman, she is constantly reinventing herself, from sexy young gadabout to wife, to mother, to carer, to, eventually, nurse.

Miller excels at describing the Russian doll-like existence of women and at showing that what you see is never the whole picture but rather one of many facets. She is particularly good on exposing what marriage and motherhood do to a woman’s sense of self. “The artist’s wife is not a professional,” Miller says. “Except that her work is her life. She says almost proudly that she has no ambition of any kind. Growing up, I knew quite a few women like that.

“My mother wouldn’t really have been one because she’d had so much of her own career, but she still did that thing of making a lovely home, being the one in charge of all social activities and cooking and generally making life so nice. It’s almost like making the artist’s life possible.

“These women create an entire universe around a man who, without them, would be rattling around in a freezing cold studio . . . It’s very underappreciated. Women now look at something like that and think, ‘Well, she’s not really doing anything’. But they are, those women – they’re making a whole world. They’re a dying breed.”

The book, she says, “quickened in my head” when she met an old friend she had not seen for years: “She’d completely changed. She’d gone from being a wild and quite reckless person to being a placid mother, two children and the wife of a man who she adored. But she was so different. I couldn’t help wondering: how do you get from A to B? Did she consciously decide to reinvent herself? If we can change that easily, who are we really?

“Marriage and motherhood mean you go from being the chief protagonist to being on the sidelines and I’m fascinated by that. Then time passes and you get back to how you were, but things aren’t quite the same.”

Miller says that American women in particular are expected to be always up, always peppy, “aggressively cheerful” and “trying to keep that energy up and be as efficient and perfect as she needs to be. It’s a manic cheerfulness that we all engage in, even though half of us might be considering driving off the edge of the world”.

In her book, the mother and daughter are both striving to present an idealised version of smiling, capable femininity to their husbands and families. “It’s a way of deflecting people,” Miller says. “You know, ‘I’m no trouble’.”

Speaking of crises of identity associated with motherhood, what about Miller herself? She is 45 and has two boys, Cashel, nearly six, and Ronan, nearly 10. “I think how you deal with that depends on the amount of repression that’s involved. For most women, the moment when they have children – especially if they are women who have an occupation – is the moment they either have to put it on hold or shrink from it, start shrinking.

“And for a lot of women that’s almost too much – life is too much and they don’t know who they are any more. I’ve seen that a lot. In my case, there was never any question that I would stop anything – but then I had a job that was very conducive to having children: writing, or even making films – my shoots are quite short and don’t go on and on, so it’s easy for me to continue because I never had to interrupt people’s lives too much.

“It becomes really difficult for the women who have desire to do both – work and family. I guess what women are allowed to achieve and allowed to hope for hasn’t changed that much. Men are still expected to do a full day’s work and so something’s got to give – and the women are usually the ones who have to take on the burden of everything, because parenting isn’t considered a call that both parents have to answer in the same way. Every time you read an article or a book about this, the solution is ‘women have to quit work’, that’s always the solution: quit, quit, quit. I think that’s terrible.”

Her novel describes movingly what old age does to powerful men: “Instead of letting go of the material world in preparation for the spiritual, all of these things like money and vanity become more pressing.” It may be relevant that Arthur Miller was 46 when Rebecca was born: she has said that he seemed very old to her (“I think a lot of kids have this feeling – you could call it a kind of premourning; asking themselves the question: what am I going to be when they [the parents] die?”).

While we are talking about marriage, I mention a phrase in the book where she says “marriage is an act of will”. Is that her view? “No, no! I was at a dinner party and I was in the first flush of my marriage and I was pregnant and this woman – married a long time, very happily – said, ‘Marriage is an act of will’. She said, ‘I could be married to anybody here – it’s a question of making a conscious decision to make it work’. I am fascinated by the notion. You create it and you make it work.”

The Private Lives of Pippa Lee by Rebecca Miller is published by Canongate Books on April 1 at £9.99

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