It sounds like you need to help your iPhone (and iOS) understand that your family members are not spammers.
First, make sure each family member is saved as a Contact in your Contacts APP.
After entering family members into Contacts, use a function inside the Contacts app to define related names. Please see the ATB (AppleToolBox) article on getting the most out of your contacts “7 Tips to Get The Best Out of Your iPhone Contacts.”
You may also want to turn off this setting To filter iMessages, go to Settings > Messages and turn OFF Filter Unknown Senders
And go to Go to Settings > Messages > Blocked and make sure none of your family members are listed here. If they are, unblock them.
Best of luck,