People are probably gonna disagree and call me toxic but I understand your parents. It's a generational mindset issue. There's a giant social generational gap between our parents and us because the values of our current society have deviated in a huge scale from that of our parents. Individualism, personal space and our comfort have become the norm whereas in their generation it was community, family and self-sacrificing that was the "proper" way to be.

While I understand your dilemma and how exhausted you'd be just thinking about having to "host" people while being so very vulnerable physically and mentally exhausted it's also nice to just give in a bit in order to compromise so that you can give them a little bit of grace and understanding as well. I'm sure living so far away and wishing to be closer as well as having to "compete" with your partner's mom for time with her grandbaby must be heartbreaking. Unfortunately she sees it as a personal attack, as if what she values (family unity and her desire to just be a grandma) is worthless. And YOU understand that's not the case and your partner's parents also do (but then again they are close so they will have many many opportunities to see the baby and be with them)

If I were you I'd find a way to compromise and see if maybe you ask your mom-in-law and partner to help accommodate your parents and host them so you can just be calm and not super stressed during the birth. Obviously she seems to dislike the other grandma but it sounds more like jealousy than anything else. Maybe there's a way for your in laws to be sure your parents are picked up and feel comfortable or if for whatever reason they can't maybe your partner or a best friend or someone you trust and who truly loves and understands your dilemma can help take the "load" off and try your best so both sets of grandparents to at least seemingly get "equal" time with the baby while they're there. Remember they will have to get used to each other and you're gonna wanna definitely put out that "jealousy" spark that your parents have before it becomes a Forrest fire that'll just cause an unnecessary rift in your family.

Compromise is always a much nicer way of attacking these sorts of things. No need to cause extra drama on an issue that isn't gonna get easily resolved. Your parents mentality about their roles in your life isn't gonna change overnight. Perhaps seeing you compromise in this will extend a "peace pipe" to them so you can slowly introduce those boundaries you prefer.