You're fine here. It's actually easier for people to keep up with your story if it's all in one place.
My daughter said I was putting her in the middle when I told her what has been happening with her Grandma and I so haven't told a soul that I know she has now seen the baby. That would upset my daughter and make my son mad at Grandma.
I'd think you're kind of "damned if you do and damned if you don't" in this situation. On the one hand, your daughter says she doesn't want to hear it, but on the other, she's putting herself out of the loop and doesn't know what's going on. She's an adult and I can understand that it's difficult to deal with feelings of both loyalty and disappointment regarding cheating parents. I felt that way too once upon a time. But you're actually going through something right now, and while it's best that you don't treat your kid like your therapist, a modicum of empathy from her wouldn't be out of place. I think it's okay to say to her that you understand she can't fully empathize with what you've been through because she lacks the personal experience and this just isn't something which translates fully to the imagination of others, but you ARE going through something traumatic and life-changing and you're doing the best you can under very difficult circumstances. She needs to decide if she wants to be IN your inner circle or out of it. That's not picking sides.
You can certainly refrain from bad-mouthing and editorializing, but at a certain point, our kids have to decide if they want an adult relationship with us. Keeping her informed of what's going on in your life is NOT "putting her in the middle". Believe me, I know the difference well. My mother used to tell me to "tell that sawed off son of a bitch that he goddam better write that check before the weekend was over" and that I better have it with me when I got back. THAT's putting a kid in the middle.
I have found out that my MIL has been keeping things from me such as the money she gave her son and now I found out WH brought the baby (not baby mama though) to meet his Mom.
Your MIL is in the unenviable position of being pulled in two different directions. On the one side, you and the grandchildren she's already attached to with the right clearly being on your side. On the other, the child she gave birth to and another grandchild who she won't be allowed to know if she refuses to play ball. Your cheating WH is quite likely to create his own narrative about "being unhappy" and God only knows what other excuses to make it sound like he didn't have any choice but to drop his pants and impregnate some immoral interloper. You know yourself though from having adult children that it's nearly impossible to imagine what they could do to make you stop loving them. So, when you do the mental math, it does seem unlikely that your MIL is going remain firmly in your camp.
I'll be honest with you, it'll drive the OW mad that you've still got a cordial relationship with your STBXMIL, so if it was me, I'd downgrade the relationship to "friendly acquaintance" and keep my own council on important matters. At that point, you just assume that anything you say is getting back to the cheaters and even use that in your favor if needs be. I once had a boss who used to get in people's faces and scream at them. I happened to mention to one of my work friends (who I KNEW would carry the tale) that if he ever yelled at me like that, he'd be finishing my shift himself. That guy would practically turn blue holding his tongue when he was mad at me, but he never said a cross word from then on.
The alternative is that you can come clean and admit that you know she lied and have a talk about the importance of honesty and all that, but your MIL is compromised and I don't see that ever changing. If the relationship were to become toxic to you, you could certainly go NC, but I wouldn't think it necessary unless she were to become outwardly abusive. Right now, it seems she's going out of her way to make you think she's Switzerland so clearly, she cares about what you think. So, heck yeah, if you want to do Thanksgiving, I'd just make a point of not discussing the cheaters and their drama. NO ONE deserves the schadenfreude of drama at your expense there.
It really does sound like there's a lot of pressure on you to conform to other people's expectations right now though. I hope you're putting together a good emotional support network. It's super important to have friends and family members who you can be real and authentic with. You'll want a good therapist too, of course, and there's here. There are so many people we have to be guarded with in this kind of situation, but having those few, key people in your corner can keep you from isolating yourself. That temptation to push EVERYONE away can be strong and it's easy to give in to it when you're not maintaining openness with anyone.
Remember that no matter how much things suck right now, it's a temporary state of being. Things are going to get better. The more you believe it, the sooner it will be.