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.

I believe you can just remove your payment info from your apple account and then have your wife add her payment info and she will be able you be the payee.

Your Apple ID is the personal account that you use to access Apple services like the App Store, iTunes Store, iCloud, iMessage, the Apple Online Store, FaceTime, and more. When you change your payment method or billing address, your information also updates everywhere that you use your Apple ID.

Or You can go to your

Settings > iCloud > Family and then tap your account. You will see an option to Stop Family sharing. This will allow you to clear this out and start over, which is what you were originally trying to do..