Tax credits are targeted at the child or children involved, generally being granted to the parent agreed to have majority care.
There is no obligation for you to hand over tax credits if you are the recognised claimant - this is cut & pasted from the HMRC website :
If your child lives with more than one person
Only one household can get Child Tax Credit for a child.
You might look after a child who sometimes lives with you and sometimes lives with someone else. You can't both get Child Tax Credit for the same child, so you'll have to decide who should get it.
You can't claim Child Tax Credit if your child doesn't live with you at all - even if you're paying maintenance.
If you can't agree who'll claim
If you can't agree who'll get the Child Tax Credit, both of you should claim for the child. Then the Tax Credit Office will decide for you. They'll contact both of you so that they can work out who has main responsibility for the child. They will consider things that include the number of days the child lives with you, and where they keep most of their clothes and toys.
If you're already getting Child Tax Credit for your child
Someone else might make a claim for a child you're getting Child Tax Credit for. If this happens, the Tax Credit Office may ask you to tell them why you think you have main responsibility for that child.
If you can't agree who should get the Child Tax Credit, the Tax Credit Office will decide for you. You'll still keep getting paid while they make their decision.