My DS and DiL had/have a similar problem, but with my son's MiL, not with me! She is overbearing and manipulative. DiL is too nice to say anything, as she doesn't want to cause any upset with her mum, and my DS just wants to keep the peace, but often complains to me about her! I once made the mistake of speaking my mind, as she had also upset me, but that caused a bit of bad feeling within the family at that time, for which I regret. Although, sometimes, things need to be said!
Whenever she visits them, she often takes over and, in the past, has disregarded routines that DiL & DS have with our GD. Last time we all visited together, I witnessed her telling them she didn't agree with the way they do things, and she disrupted our GD bedtime routine which DiL & DS had been working on. Then, when GD became unsettled, and wouldn't go down to sleep, she finally hands her back to mum/dad to deal with a very fretful baby late at night!
I do my bit by offering support and encouragement when needed/wanted, and always tell them what a great job they're doing as parents, because they are. But these days, I tend to stand back and keep my mouth shut as far as the other MiL is concerned!
It's awful when you have a bad atmosphere within a family, and I really sympathize with you. But it seems that you and your husband are on the same page as far as your MiL is concerned. It's difficult, I know, but for the sake of a harmonious family relationship, try not to let this develop into any kind of argument. Try to have a casual conversation with her, and tell her it's not easy being a new parent/grandparent, and there's lots to learn. Tell her that you know she'd like you all to join them for Christmas Day, but you and your husband would really like to spend your 1st Christmas relaxing together at home, without any stresses of unsettling the baby's routine, etc.
As someone else suggested, call and invite her round occasionally, when it suits you, but if she's not available, at least she can't say you don't invite her! When you visit her, and she takes over, I can understand how annoying that must be for you, but looking at it another way, you could let her get on with it and have a bit of a rest yourself! It's till early days, and the novelty of her new GC, could wear off over time, and she won't be quite so overbearing.
Hang in there, and make sure you and your husband stay on the same side. Hopefully things will settle down for you.