Here's an article explaining how payment works when using Family Sharing:
Family purchases and payments - Apple Support - https://support.apple.com/HT201079
"Any time a family member makes a new purchase, it's billed directly to the family organizer's account."
but it omits a critical piece of information saying an individual with account balance will have their account charged first before any remainder being charged to the organizer's account. That is clearly stated in: How App Store and iTunes Store purchases are billed - Apple Support - https://support.apple.com/en-us/HT201359
"When a family member in a Family Sharing group makes a purchase, their personal Apple ID balance is charged. If there isn't enough balance to cover the purchase, the remainder is charged to the primary payment method on the family organizer's Apple ID."
and:
https://www.apple.com/legal/internet-services/itunes/us/terms.html
"The Organizer's payment method is used to pay for any Transaction initiated by a Family member (except when the Family member’s account has store credit, which is always used first). "
So to answer your question, your daughter cannot use her credit card. She can add a gift card to her account to pay for items without them appearing on your credit card.