How to change the Organiser for Family Sharing
The only way to change the person who is responsible for the payment method (in other words, change the Organizer) is to turn off Family Sharing and have the new person start it over again.

In the Settings app go to iCloud then tap on Family, then your account in the list at the top, then Stop Sharing. This will disband the family.

At this point, your wife can go to the same location (Settings > iCloud > Family) to start Family Sharing again with her account as the Organizer. This will then use her selected payment method for any charges made by the Family members.

Your daughter's account will have to be re-invited to the family. Your wife can also invite your account and once you accept, mark you as a Parent so that purchase requests from your daughter will go to both you and your wife.