Yikes. First, people saying the house won't be yours are guessing. Children are first to inherit, but not if a will says otherwise. Much more importantly, though, it's irrelevant. Right now, you are living in hell and that's because grandma can't or won't take charge . It's her home and she runs it. Your inlaws are trash, but don't forget -- one of them is her child. Those bonds were created before you were even born.
If grandma isn't willing to kick these jerks out, you have no choice. Get an apartment with your husband. I can't imagine living with someone who abuses my dogs. The first time I saw this, I'd be gone.
Get out of this mess and do what it takes to make that happen quickly. Grandma could live another 10 years and you can't possibly have a happy marriage in this environment.
Also, it's very possible your husband might drag his feet. This is his mom and his sibs. I hope that doesn't happen, because for me, this would be a dealbreaker. His family sounds pretty dysfunctional and it may have impacted him. But I'd be leaving, with or without him. I would refuse to live in a home where my pets are at risk.