Atomic Kitten singer Kerry, 34, split from Mark in 2010, after they had daughter Heidi, seven and six-year-old son Max together.
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She has since found happiness with new husband George Kay, also 34, but is said to be clashing with her ex, after he was found with drugs growing at his home.
An insider told the Daily Star: "Kerry really has had enough. She is hoping that if Mark goes to prison in January he will drop the whole case of fighting for joint custody of the children."
Mark pleaded guilty at Bolton Crown Court after he was found to be growing £50,000 worth of cannabis.
The source continued: "The way she sees it is that if he can grow drugs in his house, then it really isn't a place for her children to be going and she is hoping that the judge will see it the same way too.
"Mark has barley seen the children for the last few years. When they first split up he would drive down south to pick them up, or she'd bring them up north so he could see them and spend tie with them at weekends and on holidays.
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"But things have been really bad between them for the last few years."
Kerry also has daughters Dylan-Jorge Rose, and Molly, 13, and 11-year-old Lilly from her marriage to former Westlife singer Brian McFadden.
The insider added that Kerry is hoping the custody hearing will go in her favour following Mark's arrest.