My DF was a tyrant in our house. He started on my kid. I told him to stop, he swore at me and tried to browbeat me, some home truths were issued, I left the house- he didn’t speak to me for nearly two months. Literally ignored me on the street.
Prior to that I was always the one to make the peace. Childhood really did a number on me. But this time, somehow, I just didn’t. I wasn’t going to let it happen again.
Eventually he spoke to DH and said ‘he may have gone a bit far.’ No apology, per se, but that was a HUGE step forward.
To my considerable surprise he didn’t ever shout at my kid again.
Now, I do regret having a full set-to. Handled it in anger, and was most certainly triggered by hearing my little son getting it over absolutely nothing at all. That was my life and something snapped when I heard him roaring and my son weeping.
Unfortunately if your dad also wants to say damaging things and you don’t want to let him, something’s got to change.
Rather than getting into a fight, which did work, but might well not have, I’d have said it might have been worth me offering a calm, clear reassurance that while he was important as a dad and grandad, certain parenting techniques - in your case, mockery and shaming - had no room in my child’s life.
I went a big bit further and laid out all the damage he’d done to us. Probably needed said but I regret the manner and circumstances. Still, actions create reactions, better that than another generation of scared kids, and like I said, never happened again.
If your DF doesn’t like hearing your views regarding your upbringing of your kids in your house, well, he’s not nailed to the floor. What’s the worst that can happen?