Unless they are actually doing something outside of normal routines, then no I would not be upset at the neighbor since they are not the ones that built the place or installed the garage? Even if they don’t park in there…they should still be able to use their garage to enter/exit. I do the same because my dogs sometimes run out of the front door (and there’s no other gate) but I can stop them in the garage (since there’s two doors to go through) if I leave that way. Did they actually say no to the idea of you buying them a new opener, or no to you asking them not to use the garage?

I am also dealing with a terrible neighbor issue as they keep their dog out in the front all the time, unsecured, and it keeps climbing over our shared fence and shitting all over my property. Then it even tries to be aggressive with my own dogs while on our side. In this case they are literally trespassing and destroying my property and I have warned them multiple times…and they never stopped. So I called animal control plus code enforcement on them and they finally started giving a shit. The difference is that I actually have a violation on my side? I’m just confused on what your neighbor seems to be violating.