In 2004 Spiteri split from Misty's father, journalist Ashley Heath, after revelations of infidelity. "I didn't see it coming. It was a lot to cope with - love, trust, judgment, big stuff. The choices you make no longer just affect you, there's a big fallout zone. I was focusing on my home life and how to make my daughter feel happy and secure, all the things that happen when couples with children split up. I wasn't the best person to be around at the time."
Their 2005 album, Red Book, peaked at No16 in Britain. "We thought we'd take a bit of time out. We just didn't mean to take so much time."
Spiteri's 2008 solo album, Melody, started as a Texas record. "I never thought I had a need to write songs to process things, but it turns out I was wrong. It all just kept coming up. It was like a frigging hairball, I'd be choking and out comes this bloody thing.
"I felt really vulnerable. For the first time, I was like, 'I don't want to write this, I'm showing too much of myself here.'
"Being in the studio with my band wasn't the place to be. I didn't want to discuss the intricacies of the drum rhythm or guitar solo. So I said, 'I'm thinking this should be a solo record', and they went, 'Phew'.
"They were just glad not to be stuck in the studio with this mental woman."
She recorded a second solo album, The Movie Songbook, with the late, great producer Phil Ramone because "it was like a once-in-a-lifetime thing, a week in Capitol Studios in LA with Quincy Jones' horn section and Otis Redding's engineer. It was a little bit of luxury."
Before the album was released, Texas guitarist Ally McErlaine collapsed with a brain aneurism. He was in a coma for nine weeks. "You get a phone call," recalls Spiteri, "and you're told he's probably not going to survive. That was a massive shock. You're not thinking about Texas at that point, you're just thinking about family."
McErlaine's wife, Shelly Poole of Alisha's Attic, "just never gave up, never gave in. He got an infection in his spinal fluids, they had to fit him with a tap, then they lost him in the operation, pulled him back, but it was like, if he ever wakes up he's going to be seriously brain-damaged. And then, one day, he opens his eyes, and his wife's sitting there, and he goes, 'All right, Shel?"'
McErlaine spent six and a half months recuperating in hospital, during which time he asked for a guitar.
"I take the guitar up, and he picks it up and starts playing. It was just Shel and me, and it was quite emotional, because the doctors didn't even think he would pull through. And he goes, 'This is shit, my hands are all stiff'. A week later, we're all up at the hospital and he goes, 'I want to go on tour'."
In 2011, Spiteri estimates that Texas played to half a million people. "And that was just bits and pieces. We wanted to take it slow to see how Ally coped, and we all totally fell in love with the band again. It was a bit like a Rocky movie, 'Yeah, come on. Let's go'." Everywhere they went, she reports, "taxi drivers would say, 'When's the new Texas record out?' So you think, 'Right, it's passed the taxi driver test, let's do it'."
The Conversation is an impeccable collection of hook-laden pop-rock songs that draw on classic 50s and 60s influences, fusing them with a sleek, contemporary drive suited to Spiteri's distinctively poised, smooth vocals. Working without a record deal, Spiteri says the whole experience felt "clean, airy and free".
She and her writing partner, Texas guitarist Johnny McElhone, collaborated with friends who included Bernard Butler and Richard Hawley. "I remember Richard looking up and saying, 'Hell, if the three of us together can't write a half-decent song, we should just pack it in'."
The album is overflowing with a sense of rock history. "You can hear country, soul, rock'n'roll, doo-wop, blues, all of those things," Spiteri, says.
"That's the music we all know and love, Leiber and Stoller, Goffin and King. There're bits of Elvis in there, Ike and Tina Turner, Roy Orbison, Nancy Sinatra, Scott Walker. I can hear Abba, too.
"When you love music it's like there's a jukebox embedded inside you. You get to a certain age when you become unembarrassed about acknowledging your influences. When you're young and in a band you're going, 'I'm a rebel', but you are thinking all the time about how you're viewed by other people. You actually only become punk when you hit a certain age because you truly don't care.
"If people don't like it, they don't like it. I've got bigger things to think about."
Spiteri is an engaging character. In contrast to her luxurious singing tones she has a feisty, abrasive, spoken style, with a strong Scottish accent and a tendency towards profanity, for which she frequently apologises. "I'm trying not to swear. My daughter doesn't approve." She comes across as a very adult person, yet her lyrical preoccupations remain pretty much unchanged from Texas's 1989 debut single, I Don't Want a Lover.
"That was the first song I wrote. I was obsessed with not just wanting physical love, I wanted mental love, I wanted my best friend, I wanted everything and the whole package.
"It's a big subject. I see it from very different angles now. You love your children and you'll never love anything like that ever. But it's funny how, as we get older, we don't talk about love. If you say to your boyfriend or husband, 'Do you still love me?' they go, 'What are you asking me that for?' But sometimes it's nice to just say the words."
Spiteri is in a long-term relationship with chef Bryn Williams.
"My life is picture-perfect," she says. "I never thought I'd get to this place. I thought I was going to be on my own, I've got so much baggage. I said to my friends, 'I'm just gonna have liaisons from now on, like a movie star.' I could have been the mysterious older woman.
"I saw One Direction pulling up in a limo the other day. I wanted to throw myself over the bonnet. 'Harry, take me, I'm yours.' Och, but my daughter would have been mortified."
Who: Sharleen Spiteri of Texas, veteran Glaswegian-born roots pop-rockers
What: New album The Conversation
When: Out now