So, I don’t think you’re having any problem communicating to him that his behavior is causing you distress. He also doesn’t seem to be willfully disregarding you either.
This is a good thing. It means that the problem is the problem, not either of you. The real issue I see here is that his family doesn’t like you. There could be a lot of psychology there that’s not being addressed. Maybe they feel like you’re taking him away from them, maybe they wouldn’t like any of his girlfriends.
If the problem there is literally that they want you to apologize and that’s it, then I’d say a sincere-sounding apology might be just the thing to get them off your backs and put your relationship back on track. But that might not be all that’s going on.
If you really can’t get along with his family, then you really need to save yourself years of heartache and just call it an incompatibility and move on. If you guys get married, unless you can take him away from all that nonsense and move to another city, then you’ll be stuck with it, day in and day out.
What I would do is to tell your boyfriend to man up and do what it takes to get his family off your back, because if he can’t, you guys are done. You can agree to apologize, just this once, to show that you’re a team player, but this can’t be coming up several times a year.
If you really don’t want to break up with him, then you need to move away. My step-dad moved another state over after he realized how caustic his mother was to his relationship. Distance has a way of making the crazy bearable.