The only way to get an Apple Card with a new AppleID is to apply again for another card. If you don’t want the card on the previous AppleID, you’d have to cancel it.
And if you’re sharing one AppleID for your families devices, that is never recommended. Everyone should always have their own AppleID for their own devices. AppleIDs are unique personal login IDs for Apple online services. They were never intended to be share and used by multiple people. For one thing, there is no privacy nor separation of data when people share one AppleID. Everyone has equal access to iCloud email and iCloud data and files, FaceTime calls, messages, notes, passwords, etc.