How does one get Apple Cards for spouse and family members?

See the following from Manage your Apple Card account - Apple Support

Only the account owner can currently use Apple Card. If a family member or friends wants to use Apple Card they will need to apply for Apple Card.

Well if the family members share an Apple ID (like my wife and I do - makes it easier for most things as she is very non-technical) then the Apple Card will show up in all the Wallet apps. However, you will only be issued one physical card at this time. (Sure Apple will change that in the future - no reason they can't issue multiple cards linked to the same account like "normal" credit cards.)

Please tell my about this "biting hard"? And what my "BIG mistake" is?

I doubt that that will change since the card is slaved to the single-user iPhone.

If you're sharing an Apple ID, eventually that will bite you hard. You're making a BIG mistake.