I know when my son went to go live with his dad for a while, I (the mother), wrote a letter to Child Family Allowance stating that my son is now in the care of his father and I would like the Child tax to be transferred to his account, for the time he remains in his fathers care. All child tax goes to the mother, unless the mother is willing to part with the child tax that she receives for that child, that is another battle. You can request it to be sent to you. If you and the mother are compliant, as always, things are way easier to sort out.
If you have expenses written down and factual information that your child lives with you, you don't necessarily need a letter from the mother. In the end, during tax season, you can state your cause if you claim that child, indicating that child is in full custody with you and the other party would have to pay back the child tax that they took from that child, leaving you getting the child family's allowance which you deserve if you have that child on a full time basis. Good luck

I hope its not messy.
(This is just what I know from past experiences, please correct me if I am wrong. But going through all this is something I am familiar with.)