I don't want to get too deep into your business but just to understand better what you're trying to communicate.... Please tell me if I get this right: there's current (not past) drama in your family and you think that not acknowledging father's day at all would feed into that drama (maybe your dad's reaction would be "see, you're all against me" and he'd play the victim or something like that) . On the other hand you also don't want to pretend everything is right with your father. So you want something to communicate "I don't want to be against you, but I certainly am not on your side either; I just want to be left alone and talk to you the strictly necessary amount of times". Is that it?

If that's the case, yes, the standard-est, humorless "happy father's day" card you can find, with nothing but your signature in it should convey that message pretty well. If you can't find anything, just a white one with a handwritten "happy father's day, [your name]" would do.