What about this: could you 'strike a deal' with her? Something along the lines of negotiation through possible concession... not in a shady way, but in a way that may make MIL feel like she is being heard.

I, too, wanted a more private time when my kids were born- and my ex's family did not like that one bit. To them, having a baby is a family affair to be celebrated by all, and they all come together to share in the joy and care of new life. Only my ex did not back me up at all and instead stood firmly with his parents (hence the 'ex'...)

For instance (even if this is not the case), saying, "That's right, we may be so exhausted and needing some alone time together to reset, we may change our minds- but we won't know how we will feel until we get there. We would appreciate it if you would give us this time, and if you are willing to give us this time to bond- just the three of us- for a few weeks, we will consider an earlier introduction".

Because, honestly, you will not truly know how you will feel until you get there. Being humble about that fact has no bearing on your eventual decision. You may change your mind and decide on an earlier introduction. Or you may remain steadfast until the 56th day and be happy with that decision.

You just don't know yet.

With the pandemic, you could maybe even frame it like this, to MIL: If both you and your sister are willing to quarantine at her place for two weeks after you arrive (which will not be until we call you and tell you baby is here), we will allow an earlier introduction. The risk to babies is not zero, and the risk to adults is considerable- if it's framed around baby's and parent's health, MIL can blame the virus for her "misfortune" instead of you...

Some people can allow for these uncertainties/differing beliefs, though, and some can't.

My ex's family couldn't and were resentful towards me because of it- well before divorce was even a thought in our minds. I didn't act 'right' and they let me know it. I don't believe the first approach would've worked for my situation. The second might have worked, but I'm sure would've left the in-laws believing I was a deranged fearmonger (which would've been okay, too). But I also never truly had my ex 'in my corner'...

It sounds like you have a good team-thing going with your husband and that's gotta be at least half the battle, right?! :)

Good luck and skill to you! Wishing you a brief labor, a joyful birthing experience, a healthy baby, and a peace-able resolution with MIL!