There's a bug in payments that has been acknowledged by Apple. If you have turned on Family Sharing and have also turned on Purchase Sharing or iCloud Storage, the iTunes store gets "stuck" on the card you had active at the time you set it up. If you later change your personal credit card, Sharing will continue to use the old card.
The only solution is to TURN OFF Family Sharing. This can be a problem if, for example, you have upgraded 200GB or 2TB and any one other family member exceeds the default 5GB. You can get around that by going on a device assigned to the account that is using over the limit and temporarily subscribe to more. That will also kick that user out of the Family Sharing. Sadly, that means you'll have to pay for a month, but it's better than losing data! Note that booting out of Family Sharing *may* get you charged for paid apps or app features that were originally purchased on the Family plan. You can contact Apple support (chat works best) to get a refund after you go back on Family Plan below.
After you turn off Family Sharing (you have to boot all members first), you can then go to your credit card and change it. With Family Sharing turned off, you should now see a "None" option to remove all payment info. Choose that first and save it to erase all old history, then go back and define the new card again. After you're happily on the new card, you can turn Family Sharing back on.
Note that until they fix the bug, you'll have to do this every time you want to change the credit card you want to use for Family Sharing.
Change Payment Method Family Sharing
