I'm not disagreeing that your husband has been really unkind, and I sympathise a lot that you don't want your MIL to stay. Personally I really struggle with my FIL so do know how that feels. But I can't help wondering if this has got really over complicated and over emotional for both of you.
Walk a mile in your husband's shoes, he loves his Mum (that's normal, right?) and though his first priority is to you as his wife she's still his Mum and, rightly or wrongly, he sounds like he's really caught in the middle here. He backed you re Christmas, he's listening to you, (and maybe he would have liked to spend it with his parents, no idea, but they're his parents, it'd be understandable). Maybe he didn't think it was such a bad idea for them to visit in Oct, maybe he just didn't know how/ think to say "no" when he got a sudden request , but it doesn't strike me as the most terrible thing to have said yes to. He can't do right for either of you, though it sounds like he is trying to find a middle ground (an Oct visit sounds like some kind of compromise suggestion from your FIL, perhaps he's been having fun dealing with your MIL) no wonder your husband is frustrated and lashing out - I'm not excusing what he's said AT ALL, I can just see how he might have got there.
Sounds like your MIL is a bit over bearing, but you're playing a part in the story too, you say yourself you keep her at arms length and have difficulties with her because your own Mum died, so do you need to think about that and is there anything you could work on and not pin it all at her door? I don't agree that your DH should be "bending over backwards for you" OP, there's two people in the relationship, they both count.
Sounds like you're doing the right thing working out how best to make the visit work. Can your husband take at least some time off? Can you have some activities that are still just for you and DD so you're not with MIL all the time? Can you set ground rules for the evening so DH is with his Mum and not you just making small talk, that does sound painful. Would you be able to have some time out just DH and you if you are happy for MIL to babysit? Is there anything MIL is good at that would genuinely be a real help - cooking, cleaning, ironing, gardening? Sounds like she's keen so how can you get her doing something that really would be useful for you? You don't have to leave her with DD if you don't want to, that should be absolutely your choice. What else could she do instead?
And for your DH, sounds like you both need to come out of the mutual "you're completely in the wrong" trenches. Your DD is only 6 months old, it's a really exhausting time, if your MIL really is one from hell (rather than a bit overbearing) you need to find a way for that not to drive a wedge between you and DH. And remember, you'll probably be a MIL one day too, it seems like a really hard role to get right, particularly with a DIL so bear that in mind. She probably has no idea, and would probably be mortified, to know that's how she's coming across. Good luck.
M