I'm going to accept that your MIL has some other great qualities or you wouldn't describe her as a "kind and wonderful woman." I also accept that your husband must have some great qualities because you love him. But ... the situation you describe, the things she says to him behind your back, and his laziness in dealing with her would have me screaming, climbing the walls, and probably committed to the nut house with the rest of the squirrels.
When you say "he tends to brush off any complaints I have about his mother as a "my wife versus her MIL and I'm staying out of it" thing," I see red flags. He should be putting you and your family first and setting his mother straight as to exactly who decides what goes on in your house (specifically not her). I don't think I would let her in my house after this: "So MIL was kind enough to inform me that since she and Grandma will be spending the bulk of Monday and Tuesday at my house, could I please have the whole house cleaned and tidied, including the master bedroom and closets and such, because the closets were messy too?" There is absolutely no reason for her to go into your master bedroom, let alone your closets. Your husband, her son, should be the one drawing clear boundaries because she is his mother. He should be protecting you from her backstabbing because he is your husband.
You are much more patient and forgiving than I am. I give your props for that, but I don't think you should continue to be patient and forgiving. If your husband won't stand up for you, stand up for yourself. You deserve to be treated better than this, especially in your own home.