Why not actually talk to your Dad about this? It might be that there are some meetings that could work for you both being there (Big Book study or Step Study for example, where the talk is about the program rather than ourselves) , and others wouldn't be so comfortable for either of you. He's likely to feel exactly the same way you do about it, so it's more a case of agreeing the boundaries about who's going where. I suspect that if you don't have that conversation you're going to be worrying that you'll bump into him, or someone who knows him at a meeting, and what he will say or think about you going but not chatting to him.
Most personal stuff tends not you be shared in meetings with the whole room anyway. That would be one to one with a sponsor, or close AA friends as you make them. No one actually has to say anything in a meeting if they don't want to, and anyway, we learn much more by listening than by talking.
I hope your out of town meeting goes well enough that you feel emboldened to chat to your father about the more local meetings.
Wishing you all the best for your recovery. BB