To think this isn't weird?

Stop. You are not divorced yet. This card makes you uncomfortable. Something like this is a mutual decision in a relationship. You clearly are unhappy with this. Don't go along with something like this which some may consider small, yet is really large. You know what you think and feel. Talk to him. Be clear. Be firm. And he should understand. Tell me something, did he assume you went along with this? Was it discussed at all? Does he pressure you in other things? I am just curious.

it is weird yes

Yep too soon.

Seems a little premature to say the least. If I were a long standing family member and you sent me one my first thought would be that either you're delusional or he was putting undue pressure on you.

Sounds a bit awkward if you are not family unit yet. Your friends and family that know him and his daughter should get a separate card from him I'd think

just because you don't live together doesn't mean you aren't a family. if everyone involved is comfortable with that it's fine

Go with the flow.