Just provide the information. It will save you a ton of ongoing misery if you will. The court can compel you to provide it, but why make them have to do that? All that does is prolong the time it takes to have everything settled.

The court will tell you that she can use that money for rent/mortgage and utilities in order to keep a roof over the child's head when he/she/they are with her. She would be told the same thing about you if she has to pay you, as well.