NTA You don't have to give in just to stop your mother and sister harassing you. Go low/no contact with them and protect your son. It's possible she could involve your son some way, or he could get stuck in the crossfire, and it doesn't sound worth it. Make your life simple and peaceful.

she tried to do more activities with him in the last month we've been no contact than the last 6, when everything was ok.

This sounds suspicious, like she's doing it with some ulterior motive. Your sister sounds like she enjoys poking at you to get a reaction, and isn't above using your boyfriend and son as indirect ways of getting at you. If you think this is the case, then just put a stop to it. Pull the band-aid off, weather, the backlash, then get on with a peaceful life.