It would have been better for her to buy a small flat.
If she has her own sitting room, make sure you keep to your sitting room. There's not much you can do about the kitchen but don't use it as a social space, just for cooking, maybe eating if you have to but not when she is doing her food. Hopefully she has her own kitchen cupboard; her own little fridge and freezer would be a good idea if you have the room.
I presume she does her laundry separately, that shouldn't interfere with you.
Tell your children their grandmother needs her privacy so they are not in and out of her room all the time. Obviously they'll see her sometimes, so they should, but the point is they don't live with her, they live with you and their dad. There are two separate households under one roof.
Make sure your husband is behind you in this and enforces it firmly but gently.
If none of that works, threaten to leave. I wouldn't put up with it.
There's a lot of racism/xenophobia about at the moment, more so than a few years back and particularly amongst elderly people. It's vicious, horrible. I should know, I am 75 :-). I hear a lot around where I live and, frankly, cannot wait to move, consulting Rightmove is my current hobby. However I wouldn't have thought your mother in law was that old.
You'd be within your rights to say you don't want that sort of talk in front of your children who are impressionable. They will hear it from others as they go about life but they shouldn't hear it in their own home. I used to insist on that years ago.
Good luck.