Sigjuice, I just intentially messed up our iPhones and then went through the process again and was able to fix them again by removing the email addresses and phone numbers that allowed me to remove them. The email address you cannot remove is likely your Apple ID, so uncheck this email address.
Remove everything else that can be removed and uncheck those that cannot be removed.
Touch your Apple ID and this should give the option of signing out. Do sign out.
Then disable iMessage.
Then turn on iMessage back on.
Sign back into your Apple ID.
Select your iPhone phone number or add an email address that is NOT your Apple ID. YOUR iPhone and iPad MUST use the same phone number and email address. I used only my iPhone number and no email address.
Do the same for your other family member's devices each using different phone numbers and email address. from the other. However, Mom's iphone and ipad MUST use the same phone number/email address and so on. This will work, please let me know the outcome.