Hello Mfelts,
Sign out of ICloud on the devices using the old ID and sign in again with the new.
Click on this link to learn how to 'Sign in with your Apple ID' --> https://support.apple.com/HT204053
If another Apple ID is signed in you may need to enter the password for that ID to sign out of that ID first.
Related to this are suggestions in this document: "What to do after [or before] you change your Apple ID [email address] or password" --> https://support.apple.com/HT204071 - "After you change your Apple ID email address or password, you might need to update your sign-in information with any Apple services you're using." - Or if you're seeing persistent disabled messages or repeated requests for the password to your previous Apple ID. You may also wish to turn off "Find My" before changing information and turn it on again afterward.