Let's do a scenario analysis. Others can chime in if I'm missing something.
Scenario 1. You go and he goes. You both want to be with your mother on the holiday. You both have equal access, and it shows that he can't control her access. It's a draw until she decides that he has to go.
Scenario 2. You don't go and he goes. It shows him that he can further control your mother just by showing up. He limits her interaction with you, and he wins. I don't think it'll force a long-term breakup, so there's no direct win here other than maybe a short-term win by creating Scenario 3.
Scenario 3. You go and he doesn't go. If he doesn't go at your mother's request, it may put her more at risk for abuse later, though I think it's a long-term win. However, it probably causes her some short-term resentment toward you and won't do anything to solve the long-term problem. It's a win for you, but with some damage.
Scenario 4. You don't go and he doesn't go. Your mom eats a bunch of turkey and falls asleep on the couch during the Lions game.
Welcome to NFL Sunday! At 11:00 see Peyton Manning flip off the top rope and clothesline Clay Matthews! At 2:00 Drew Brees will hit Terrell Suggs with a chair! Buy your Andrew Luck jersey and let's get reeeeeady to rummmmmble!