You say you can't force your mother to do anything, and of course you can't. But I hope you can talk to her a/b this, and tell her you've also spoken to your DS.
Then I'd talk to DS about manners, respecting his grandma, etc. And tell him you've spoken to Grandma about it too.
Then, assuming you trust your mom with your children (regardless of her lost temper in this situation, which IMO can happen to anyone) I'd send them out on an errand together to practice their manners and to make up to each other. They don't have to know that that's what you expect them to do, but if they have a generally good relationship, I bet that's what will happen.
I remember being sent out grocery shopping with my Grandma after I threw a fit at her house b/c she didn't have anything I wanted to eat. My mom figured one long, drawn out grocery trip w/a slow old lady would cure me...and it did.