My daughter is the organizer for our family Apple account. I'd like to remove her, my credit card is attached. Can I do this without accessing her phone or do I need to cancel my credit card and create a new apple account?
TLDR; Don't cancel your AppleID, Do suspend the card or ask anyone using it to replace it whether they are in a family group or not. Then sort out the family sharing group - any account can leave at any time on their own. Then make a new group with the new organizer. Repeat leaving and joining as needed
Since only the Organizer can disband the group, individuals may have to leave if the organizer is unavailable or unwilling to act. When this happens, only a temporary loss to updates of apps happens - no data is lost. Keep each account intact - no need to make new accounts unless someone is sharing an account and needs their own personal AppleID.
To switch the grouping - have the "soon to be new" organizer AppleID leave (voluntarily any account can leave or by having the organizer remove them). Then the new organizer makes a new family group as them as the new organizer.
At that point anyone is free to choose to stick with the old group or join the new group and when I say anyone - that's the action taken by each AppleID.
Billing needs to be sorted out on an account by account basis. Each AppleID has billing - and if you are not in control of that AppleID or can't wait for them - you have to cancel that card or suspend that card temporarily. This can happen no matter who is in the family group, or whether an account is an Organizer / Parent or member of the group.