Have you gone to marriage counseling? If not, I highly suggest it. I have a uBPD/unpd MIL and I have two DD's (9 and 4). We were NC with MIL for 3 1/2 peaceful years, but since then DH has reached out to her and she sees DD4. DD9 won't see her as MIL ran me down to DD9 when she saw her a few weeks ago, and DD9 knew she was lying and being inappropriate.
Lately, my husband asserts a firm - unwavering insistence that she will visit to see our child at least once a week. He refuses to postpone a proposed visit even when I am too exhausted to entertain (I'm pregnant and have a baby), etc. He has never been this insensitive in our marriage and she has never gone for more than a week and a half without seeing her grandchild. Although I propose convenient times for visits, the more I observe her behavior and inappropriate comments, the more concern I develop about what kind of influence she will be in my children's lives.
To me, it sounds like your DH is working to please his mom to keep the peace. My DH has always done that and so does BIL. IMHO, they were raised to be her caretakers, not the other way around, which to me is very odd. So, everything revolves around MIL being happy. DH and I have been to a T before as well as two pastors who have both told DH that when you marry someone, you then 'cleave' to them and leave your mother. To me, it doesn't sound like your DH is doing this. But, I don't think he's doing that on purpose... .it's the way they are raised. It's not you that your MIL doesn't like, it's the position in the family. You took her son away from her... .that's how she perceives it.
Once a week is a lot. Even when we got along with my MIL she saw DD9 at best 2-3 times a month. Now, she sees DD4 maybe 2 times a month. To me, that is more than enough. My mom lives 15 minutes from me and maybe sees our DD's once a month. My MIL loved my DD's when they were at an age where they gave her lots of attention... .she loved the ages between 3-6, because she can get them to focus all on her. It sounds like your MIL is using your child as something to please herself... .she needs the attention, not your child.
The advice I have, from what I've learned?
1. Don't say bad things about his mother to him... .let him begin to see that for himself. If you do, he'll eventually get really angry and blame things on you. That is what happened to me. When I step back and let him take the brunt of her craziness, it is much more painful.
2. Go to a marriage T... .sometimes they can point out the obvious in a much better manner than we can. It meant a lot to my DH when our T told him the behaviors his mom had were not normal. Remember... .your DH grew up with his mom... .to him, this might seem normal. It sounds like you need to set some clear boundaries with respect to visits and such. A T can help you to navigate that.
3. Plan a spa day or something when you know she's coming over... .take a break from your child for a few hours and pamper yourself. That way, you don't have to deal with her. You could even just go to a bookstore a read a book or go hang out with a friend.
Sorry you are going through this. Dealing with a MIL like that can make you crazy.