“It can get pretty lonely just hanging out with your kids all the time,” says Missy Higgins. “It’s a bit heartbreaking feeling like [a new relationship] might be something that’s really hard for me to do for a long time.”

We are walking alongside the Yarra at Collingwood Children’s Farm, a rural oasis in inner-city Melbourne. This was not Higgins’ first choice of meeting spot – but when it became clear that her suggested location further south along the river was currently a construction site, the Guardian proposed the farm as an alternative.

Awkwardly, it turns out Higgins actually got married here – so it’s “a slightly strange [venue] for [an interview] about my new divorce album”, she laughs.

But Higgins takes it in her stride. The farm is also where she came to do prenatal yoga while pregnant with her kids – Samuel, 9, and Luna, 6 – and where she filled long hours with them as toddlers, “patting the guinea pigs and milking the cow”.

“This whole area just has so many beautiful memories,” she says. “I mean, to be honest, my wedding is a beautiful memory, too.” Down the hill towards the river is where she and ex-husband, comedian and playwright Dan Lee, said their vows in 2016.

“We all danced in the barn afterwards. It was the best fun,” she says with a smile.

Higgins rose to fame after her older sister, Nicola, entered her song All for Believing – which Higgins wrote for a year 10 school project – into Triple J’s Unearthed competition. She won, and went on to release her award-winning The Sound of White album in 2004. She has been a fixture in Australian cultural life for more than two decades.

Her new studio album, her sixth, released on Friday, has been billed as a kind of sequel to The Sound of White, which traversed the emotional turmoil of love and life as a 20-year-old. Now, in The Second Act, she tackles the breakdown of her marriage in 2022, the tears and fears of single parenthood, and her struggles to explain to her kids why their dad no longer lives with them.

The lyrics in her new work are a gut-punch for anyone with experience of family separation.

“You’ve been asking lots of questions lately, trying to figure out / Why the endings in your books don’t match ours,” she sings to Luna in A Complicated Truth.

“And it breaks my heart trying to find some words you’ll understand / ‘Cause, baby, nothing about this was in the plan.”

Just like her lyrics, in person Higgins is incredibly open about her personal life. Her responses to questions are candid, and while she is in the middle of a whirlwind of interviews to promote the new album, nothing about what she says feels rehearsed. Within minutes, she is speaking frankly about her shame and grief at the end of her marriage and the fact that she is still figuring out how to pick up the pieces in its aftermath.

“I think it’s just my art,” she says, of her disarmingly public intimacy. “It’s what I’ve always done, ever since I was a teenager … I’ve used my lyrics to kind of get to the bottom of a very difficult emotion and untangle it.

“When I sing these songs to an audience, it feels like it creates this connection between us, because I can feel the people that relate to the story and I can feel how it opens them up, too. And I can feel the gratitude that somebody is saying this stuff out loud.

“This is the most personal album I’ve ever released, but I think it’s on an accumulation of a couple of decades of doing that, bit by bit, and realising that there’s nothing to be afraid of.”

Her new songs don’t just lay bare her own deeply personal experiences – but those of her children and ex-husband, as well.

She says she is lucky to have “a really good relationship” with Lee, and that he listened to the songs before they were released.

“I thought he’d get really emotional and maybe even a bit defensive,” she says. “But … he thought it was very fair and two-sided, and that a lot of what I said was really beautiful.”

Of her children she says they are not that interested in her career or the fact that she has a public persona: “They just want me to stop singing so much around the house.”

In seriousness, she adds: “I don’t think they have any concept of the fact that I’ve just written a whole album about [the divorce of their parents].

“My daughter is very inquisitive – that’s why I wrote [A Complicated Truth] for her. But Sammy doesn’t say much, he’s a boy of very few words. I feel like maybe all the questions will come out one day, but they haven’t yet.”

As we walk past the Abbotsford Convent, where Higgins takes her children for outdoor movies on clear nights and markets on summer weekends, she says the transition to single parenting has been harder than she imagined. With her schedule, touring the country, her parents help out with the children on weekends, and “they do have a really close relationship with their dad”, she says. But they have learned they cannot have one-on-one time with her as much as they might like now that she’s a single parent, and they’re still “not that happy about it”.

“I also just feel ill-equipped to do it by myself,” she says. “I feel like I have enough love, but … I feel constantly torn between the two of them and I just wish there was somebody else in the house who could go and sit with my son and read him a book while I’m, you know, getting my daughter dressed.”

Into this complicated dynamic, Higgins has tried to imagine introducing a new partner. In You Should Run she sings to a new lover about the reality of her situation: “I come as a package, got the heaviest baggage.”

The song is a powerful take on the push-pull of single motherhood – and the fact that her “absolute priority” is always going to be her kids.

“It’s definitely been really complicated trying to contemplate moving on … and opening up my heart to somebody else when I’ve got these two little things that are my responsibility and the loves of my life, who are my number one,” she says, gazing out across the paddocks.

“It feels very tricky to bring another person into that. And I guess the song is about being upfront about that.”

For a “good six months to a year” Higgins says she tried dating, but found it too exhausting to fit around her work and family life. So while she misses “that kind of adult affection side of things”, she says she has put it on the back burner for now.

“At the moment I’m really happy having just a couple of those burner plates on – you know how you can’t have them all [on] at the same time? I’ve just switched that one off and it’s actually a relief.”

For now, she says, “I’m so happy being single. Which is a nice feeling.”

• Missy Higgins’ The Second Act is out now