Chamonix re "I know, but I look to the outside world like such a mean horrible person if I shut them out, because they're good with dd but bad for us."
PLEASE stop worrying about what the outside world thinks of you. It is a mistake to twist your life into an uncomfortable shape to please everyone. In the end you will have no real sense of what you even want.
"they're good with dd but bad for us." That REALLY means "they' LOOK good with dd but ARE ACTUALLY bad for ALL OF us."
Anything that makes your mum dread something happening, that makes your mum unable to put up proper boundaries around herself and around you, that makes your mum unhappy and causes tension between your mum and dad, is bad for you (the you here is your dd of course).
Re "I worry all the time they'll manipulate her when she's older, but is it my place to assume they will and shut them out?"
YES, fucking yes. They are doing it to you, they have done it to their son, so why would they not do it to her?
I am not a counsellor, trained or others. But I ahve had counselling a lot, for a lot of isses (anxiety, fertility issues, eating disorder) so I am not an expert but if in doubt speak to a consellor and get some advice.
So as a non-counsellor, who you are totally free to ignore, I think, you and dh need a heart to heart, and to decide YOUR OWN boundaries as a coupe in relation to your in laws and your dd and your wider family. Then you need to put your dd somewhere safe for an hour ot two (your mums?) and meet your in laws face to face at their home or on neutral territory. I think you need to say to his parents that this Christmas thing has brought up a lot of issues about boundaries.
I have no idea how old your in laws are or how savvy they are with modern ideas, and the idea of boundaries in families may go over their heads.
So I would probably say things like...
We (as a family, dh and you) do not feel respected by you, (in laws)
When we make choices and decisions we feel these are walked over, or we are challenged to change the plans we made.
When we do not change plans to accommodate what other people want, we feel that there are tears and stress and we are made to feel like the baddies.
All this is proving to be very stressful for us and is affecting our daughter.
We need you to listen to things we say about what we will do, when we are free to see you, when dd is free to see you etc etc
We are happy to discuss things but when we feel you are not listening to us or being respectful of our wishes we will simply have to stop talking about it and continue with our plans.
If your mum phones up full of glee at getting an invite, please be honest and say you do not want your in laws at the family party, you have tried to make this clear.