Signature matching is a notoriously weak verification, especially when the risk is within-family disenfranchisement. You almost certainly know your spouse's and parents' and children's signatures, you likely have signed in their name in various occasions before, so signing with their signature in a convincing enough way to fool a ballot counter who gets to spend probably ~10s at most on every mail-in ballot is extremely easy.
Not to mention, you can do the opposite: you can destroy your "wrong-minded" family member's ballots to prevent them from voting.
You can always still go vote in person at a polling center, even with all-mail voting they always keep a few open just in case someone loses or spoils their ballot.
They'll record the vote provisionally just to make sure you're not trying to vote twice, and once it's clear no mailed-in ballot arrived it gets counted.
I know my spouses signature and I definitely could not copy it for the life of me. I'm sure we could put it different safeguards and they would almost certainly disenfranchise orders of magnitude more legal votes than fraudulent ones given the scale on which we've proven voting fraud to happen.
Not to mention, you can do the opposite: you can destroy your "wrong-minded" family member's ballots to prevent them from voting.