I'm confused.

It's your DAUGHTER'S birthday?
Get her a gift from "Dad".

And your daughter's IN LAWS????

That has nothing to do with you and your wife - but if you're all close or something, get them something that's just from you.

If you mean YOUR in-laws - call them and say Happy Birthday.
That should be enough unless you TYPICALLY do something special in which case the burden does not fall on you because you are SEPARATED from their daughter. It falls on her. You can just make a phone call and i'm sure that will mean a lot to them. Avoid talking about the relationship though.

Regardless of how all that plays out, your wife needs to stop picking and choosing which parts of real life she wants to participate in.

She can't just galavant all over town as if she's single one minute and then when something that requires money comes up, suddenly get to be part of a "couple" again.

Keep it real.