03/13/2008 at 07:00 AM EDT
channeled her pain over the breakdown of her parents' marriage into her music, her father says.
Mitch Winehouse, 57, reveals in a new interview with the BBC that soon after Amy's birth in 1983, he began cheating on wife Janis with a co-worker, Jane, who became his second wife in 1996. Amy and her brother Alex (born in 1980) knew about the long-running affair.
"The children used to call Jane 'Daddy's work wife,' " Winehouse says on the program One Life: Rock Star Parents
, to be aired next week.
He said he should have left the marriage sooner, and when he finally did Amy "definitely became a lot more independent. ... I thought Amy was over [the affair] pretty quickly – in fact it felt at the time Amy felt no effect at all. Maybe she could not articulate it in words, but she certainly did it with music."
He says her angry song, "What It Is About Men," refers to his behavior.
"It is easy for me to say it is my fault, and that had I been a better parent this would not have happened. But who knows whether it would or not?" he says.
Winehouse also says his daughter's alcohol and drug abuse caused a seizure in August. Further attacks could be life-threatening. "She could die horribly. That is not going to happen – that cannot happen," he says.
He is reconciled with Amy, whose husband Blake Fielder-Civil is in prison
on charges stemming from a pub fight. Both her parents and her brother were with Amy for her Feb. 10 appearance via satellite at the Grammys, where the singer thanked her family
for their support.