The reality star has also banned Croft from the home she shares with new boyfriend Steve Alce, after Croft complained about her discussing the romance in interviews.
"It was a very bad row. They have had their bust-ups in the past but he just lost it over Kerry bringing up all the drugs stories again and all the details about their marriage," a friend of the former Atomic Kitten member told the Sunday Mirror.
"Before the row, she was happy for Mark to come to the house to see the kids but that has all changed now. She told him he can't come to the house, which means he can't see the kids. Kerry is a good mum who doesn't want them not to see their dad.
"But the row was so bad she doesn't want him at the house. She hasn't seen or heard from Mark since February 17. He has sent a couple of texts for the kids to the nanny's phone but he didn't call or try to see them at Easter."
Katona, who has two other children with Brian McFadden, is planning to write a book about her "dark" years with Croft, discussing her battles with drugs and depression.
Croft is now working in a sandwich shop and has been with girlfriend Kelly, 23, for two years.