It's three months since the death of Rufus Wainwright's mother, the Canadian folk singer Kate McGarrigle, and the grief is still written all over his face. I was nervous about bringing her up in conversation but needn't have been. As we talk he returns to the subject of her death compulsively, his eyes glistening with tears.

Kate was, he says, the linchpin of the sprawling singing dynasty that also includes Rufus's sister Martha, his estranged father, the '60s folk sensation Loudon Wainwright III, and his aunt Anna, Kate's sister and the other half of the folk duo the McGarrigle sisters.

"As death approached she got more withdrawn and very concentrated on simple things," he observes. "She was quiet; she didn't want huge conversations. She was the youngest in her family as a child and she kind of regressed back into that position. Day by day she became more childlike as we tried to bathe her and feed her. There was this gentle return to an embryonic state. It was kind of amazing."

The family, and close friends including Emmylou Harris, were gathered around her hospital bedside when she died, singing songs together and playing old recordings from the past. Her funeral in Montreal's Notre-Dame Basilica, at which both Rufus and Martha sang, drew a congregation of more than a thousand mourners.

Rufus's first opera, Prima Donna, made its debut at last year's Manchester Festival and he is glad that his mother, who was his biggest critic, got to see it. "She loved it, which was obviously a relief," he says with a grim chuckle. He was similarly locked in a race to finish his new, sixth album, All Days Are Nights: Songs for Lulu, last autumn so he could devote himself to looking after her.

He has described the album as "essentially mourning for my mother while she was still alive" – she had been diagnosed with a rare form of cancer in 2006, allowing him plenty of time to contemplate her end. It's an uncharacteristically stripped-back piece – just Rufus and piano – and is also unflinchingly, heart-wringingly personal, from 'Martha', in which he begs his sister to visit their mother, to the devastating melancholy of 'Zebulon' ("my mother's in hospital, my sister's at the opera/ I'm in love again but let's not talk about it").

Baring all is, of course, in the genes. The Wainwright clan have long been known for airing their linen, often with savage candour, through their songs. Loudon, who walked out on McGarrigle when his son was three, began the tradition when, on noticing his infant son's thirst for his mother's milk, wrote the song 'Rufus Is a Tit Man'. Later he would write a song, 'Hitting You', about the first time he struck Martha as a child. When Loudon and Kate were divorcing, it was Kate who found solace in song, penning the acidic 'Go Leave'. Rufus then heaped scorn on his father with 'Dinner At Eight' ("Daddy, don't be surprised that I wanna see the tears in your eyes"), though, in a customary display of one-upmanship, Martha went one better with her ode to dad, 'Bloody Mother Fucking Asshole'. Does Rufus, I wonder, ever wish he and his family had kept a few things to themselves?

"I'll be honest, I worry sometimes about what I've done," he reflects. "I have tied my whole person to my art and, whatever it takes to get that hook, I will go there and do it. These personal, meaningful, dramatic events feed into that directly. Maybe all of us have sacrificed too much with our songwriting but the die is cast and I do think that where you'll hear a song where we attack one another, there'll be another one where we try to reconnect. Our family is a battered ship but it's still afloat."

Now, following the death of Kate, and the premature birth of Martha's son Arcangelo just 10 weeks before his grandmother died, Rufus wonders if there will be "new rules" in how they relate to one another. Certainly, there has been a reconciliation of sorts with his father, who was at Kate's bedside with the rest of the family when she died. (Loudon won his first Grammy Award on the night of the funeral, which he dedicated to his ex-wife while thanking her for teaching him the banjo.)

Wainwright also admits to being chastened by the birth of his nephew: "One of the main destructive forces within our family has been these runaway egos. I think if you look at any showbusiness family, that struggle exists. In meeting this child who has had this amazing and dramatic voyage so far, I was humbled. When such a delicate force arrives you really have to change who you are."

It's also rare to find Wainwright talking about his sister, with whom he has always had a tense rivalry, with such tenderness. "Martha has astounded me in how brilliantly and classily she has been throughout this whole time," he remarks. "She's fearless – with the baby, with everything – to the point where I worry about whether she's really taking care of herself. She went from being free, touring and singing Piaf songs to living in a big house with a baby without her mother. I really have to be there for her."

Not so long ago it was Martha who had to look after her brother in his hours of helplessness. These were the days of the party-loving, sex-crazed, drug-addled Rufus, a man basking a little too much in the praise being heaped on him and slowly losing the plot. I first interviewed him in 2001 and, though I was unaware of the crystal meth addiction that would leave him temporarily blind, I remember him being skinny as an eel, hugely narcissistic and maddeningly distracted. Now, despite the strain of the past few months, Wainwright appears focused and serious. Though he has retained his louche good looks, he has very clearly grown up.

Wainwright can't remember much of that period now, referring to it as the time when he "nipped out for a bit". Realising that he could end up permanently damaged or dead, he sought the advice of Elton John, who dispatched him to a rehab clinic in Minnesota.

He has seen a therapist on and off ever since, though he says it's his relationship with the German arts administrator Jörn Weisbrodt that has been most effective in keeping him on an even keel. Work has also kept the demons at bay, and in the last seven years he has not stopped. Following his critically adored albums Want One and Want Two (released in 2003 and 2004 respectively), there was his recreation of Judy Garland's 1961 Carnegie Hall concert in 2007. Last year, in between working on his opera and tending to his mother, he somehow found time to compose a song-cycle of Shakespeare sonnets at the behest of the US playwright-director Robert Wilson for a performance in Berlin (two of these sonnets appear on his new album).

The drama of his drug addiction has proved rich songwriting fodder, though his troubles go back further than the first flush of success. Though there were moments of great joy during his childhood – he remembers Christmases being beautiful – there were also moments of terrible darkness. Staying with his father in London when he was 14, he got talking to a man in a bar who later raped him in Hyde Park. After the rape his attacker then tried to strangle him. Wainwright believes the only reason he survived the attack was that he faked an epileptic fit.

His parents' lack of acceptance regarding his homosexuality still rankles. "I love my parents, and we have worked on this, but it was a nightmare. To be fair to them, I was very young and it was bang in the middle of the Aids era. It was 1987, and it was seen as dangerous to be gay at that point. Looking back, one of the things I love most about my mom was that she never, ever relented. She stuck to her guns right up until the end. She wasn't abusive but she was never that thrilled that I was gay. But she still hung out with me and certainly enjoyed all the trappings, I'll tell you that much. The trips to Venice, the shopping in Paris, she took full advantage of all that!"

Wainwright has just started a solo tour in which he plans "to really go for the jugular, emotionally".

Meanwhile, in personal terms, he is looking forward to a time of "acceptance and freedom from pain". In the aftermath of his mother's death he is still not good at being on his own: "Unless I have my aunt or my boyfriend to take care of me, I'm a little pathetic."

The hardest times, he says, are the glimmers of happiness. "I'm doing all these rehearsals now, and things are going so well. At the end of the day I think, 'I've got to call Mom and tell her how it's going'. That kind of stops me in my tracks. Then I have to face the undeniable fact: she's gone."

Rufus Wainwright plays Dublin's Grand Canal Theatre on 28 April