It sounds like your daughter is quite young, if this is his first father's day. And he seems to be really into fighting with you.
Look, you can't go right here. If you do nothing, he can fight with you for ignoring him. If you do anything, he can use it to start a fight about his involvement. If it were me, I would go minimal - save your energy. If you feel like it's cold to do absolutely nothing, send a text. I wouldn't go further.
If your dd was aware of the holiday, I'd say help her pick out or draw a card. Don'tmake it a big craft project, and if she's not into it, hit the greeting card aisle and pick something generic.
I'm sorry he s this way. He sounds exhausting.