I think it’s ridiculous that your DH and DM are that uncivil, that your two young daughters are saying that they don’t want their Grandma to come because it will put Daddy in a bad mood! (Which infers that your dd’s would like their Grandma with them!) When I had contact with my in-laws, despite a history of awful behaviour on their part, I put on a smile, was friendly and encouraged a good relationship with my dc. Unfortunately things later snowballed but even after cutting contact, I made sure to tell my dc that my in-laws love them very much and that our fall out was not in any way their fault.
I am wondering if your DH is emotionally abusive? It sounds like your DD’s are walking on eggshells and desperately trying to please your DH. If he is abusive and this is why your DM has fallen out with him, then I think you need to ask yourself whether you would want your DD’s to be treated the way their Father treats you. Unfortunately, having an emotionally abusive DF makes it more likely that a girl will grow up and choose similarly abusive partners.
Is your DM overbearing? Is she controlling over you? Or is she just being overprotective over her daughter and granddaughters? Either way, your marriage does not sound a happy one, unless I am misreading your posts. Apologies if I am!
Two books that might help are;
‘Why does he do that?’ By Lundy Bancroft or
‘Toxic Parents’ by Susan Forward
It is hard to know what advice to give without more knowledge of the relationships you have with both your DH and your DM.