Don't know what the laws are there in the UK, but here is the states once the child hits about 10, they have a say in who they live with. Also, unless it's court enforced visitation is not mandatory for the secondary care provider. What's really funny about it is, one of the parents could be paying child support and still not have visitation due extenuating circumstances.

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"BOY: On a hot summer night, would you offer your throat to the wolf with the red roses? GIRL: Will he offer me his mouth? BOY: Yes. GIRL: Will he offer me his teeth? BOY: Yes. GIRL: Will he offer me his jaws? BOY: Yes. GIRL: Will he offer me his hunger? BOY: Yes. GIRL: Again, will he offer me his hunger? BOY: Yes! GIRL: Yes. BOY: On a hot summer night, would you offer your throat to the wolf with the red roses? GIRL: Yes. BOY: I bet you say that to all the boys!" -Meatloaf