Hello savanah,
I think I understand what you want to do. The only ways I can think of to achieve what you want to do is for you to set up Family Sharing. This would give you control over what your daughter does and buys. However, if her father is not part of the sharing group then only you will have power to approve what she buys. You can have a second person on the approver list but then that second person has full access to the Family Sharing features which it sounds like you do not want.
There's one way you could manage his payments with his card but it involves very complex management of primary payment methods and checking personal account balances. The by far easiest way would be for her father to simply add balance to your daughter's account, for example by buying her an iTunes gift card (make sure he chooses his cards correctly as Apple may have different kinds). The Family Organizer would still have control over approving purchases but as long as your daughter always has sufficient balance in her account to cover her purchases then her balance gets used first when she buys something.
I will provide links to various Apple documents discussing what I mentioned above.
Set up Family Sharing - Apple Support
Approve what kids buy with Ask to Buy - Apple Support
How to redeem your Apple Gift Card or App Store & iTunes gift card - Apple Support
Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support