<cracks knuckles>
Been there (although multiply the distances many-fold) and have the scars to show for it. Until this year (and only because MIL's feeling the strain through age and has said she can't do it anymore) Christmas has been a time of anger and upset and disappointment and frustration and, frankly, misery because she insists on having it at her house, I insist on having it at my house (everyone welcome) and my DH is stuck in the middle. (My parents live thousands of miles away and we've never seen them for Christmas 😥). It's been awful, every single year (and it's been many years). I just don't want to spend every single Christmas at her house when I don't want to, need to, and can do a much more enjoyable job myself (they're very welcome to come to us, always). She just want to play Lady Bountiful, the uber-matriarch, at all times.
Don't be me. Don't waste those years and those Christmases.
While your baby is little I would go between your parents' house and your in-laws' house. Your parents deserve to see you and their grandchild as much as your in-laws do. Just look at the bright side: no need to host, no mess in your house, just being hosted. The travel is worth not having to host your parents and in laws at the same time given how close they all are.
When your child is old enough to express an interest, be more forceful.
Do either of you and DH have siblings? You'll have to take them into account too.
Basically, all grandparents should have someone around them whether in their house or someone else's, and no grandparent gets to dictate. NO GRANDPARENT GETS TO DICTATE.
As for dealing with your DH, I can honestly say that Christmas is the only tension in my otherwise happy and harmonious marriage. I don't blame him, but there's nothing I can do about it (being a doormat isn't an option for me). I take succor from the fact that I'm the one being totally reasonable and MIL is mental (many threads on MN over the years about her).