My House My Rules - How do I (31 F) deal with entitled Father (50's M)?

There's a lot of history between me and my father.
He's always been a phillandering, misogynistic, self-important blowhard that always needed to be "right." My sister and I (but almost never my brother) always had tons of invasive, arbitrary rules that he justified by saying "my house my rules." It just meant that the two of us stopped going to his house as soon as we were both able.
The thing that rankled most was that my brother was always able to have girls stay over since he was a teen. My dad even made a basement suite with a separate entrance for him, so as to avoid disturbing him. My sister and I weren't able to have a boy come over, even as friends. Or, if we did, he had to leave by dark (which is like 4pm in winter.) Again, the justification was "my house my rules."
Anyway, he facebooked me a couple days ago to inform me that he and a female "friend" are coming to stay in our guest room. I know from the grapevine that current wife kicked him out because she found out about his side piece, who also happens to be married.
I told him that his "friend" has to leave before it gets dark, and he needs to book a hotel room for her to go to before he can stay with us. He tried to argue, but I told him "my house my rules" and hung up. That's that, right?
Well dad's been stirring up his side of the family about how I "abused" him, and I keep getting dozens of messages a day about how I need to respect my father, family needs to stick together, etc. My grandmother has taken to her death bed (again) because her "heart can't handle being broken like this." Funny, because she's managed just fine without a heart all her life.
My brother has left me at least 5 long, rage-filled, messages about how I've turned my back on family etc. In the same messages he also rants about how difficult I'm making my brother's life because now dad's staying with him, and he's a terrible guest.
I'm tempted to just cut them all off. But my grandfather, who is the the most decent person ever, actually is on his deathbed. As in he only has a few months left, if that. And my grandmother controls access to him. Getting around her is really difficult.
Also, my kids are very close to a couple of my cousin's kids. There's no way to cut off my family and preserve those relationships.
TL;DR I guess I'm just looking for a way to smooth things over with my family, at least until my grandfather dies, without having Dad and his new chick stay over at our house.


Source.