We need to know why the newborn visit was requested for that particular day.

It's not ambiguous, the way you wrote it you are clearly the parent of the birthday child. And yes, the birth of a grandchild and that mom's request for her mom to come see her overrides a birthday party for a different grandchild.

This is assuming it's within the first week of the new baby's birth. As you surely remember, new moms need a lot of support and have a lot of hormones. She's asking for her mom to come help her. Her mom saying "well sorry, I have plans" is strange.

Now if the baby was born a month ago and the timing of this ask is on purpose to ruin your party, then that's different.

OP here - in response to 23:11

The ask came on the day of the birth - but child does not ask you to come that day but the following day, which falls on the other grandchild's birthday. Child is assuming that the answer will be yes to a visit at the requested time.

The child giving birth does not want to immediately have multiple visitors with the newborn due to concerns about illness, probably will be a few weeks before sibling and their family will meet them. Grandparent is the only one invited to meet them right now.

History: Two kids get along ok but are not particularly close. Can go months without talking, but haven't really argued. They haven't seen each other in person in a couple years but do a group FaceTime holidays. Their older kids have met once or twice.

The child with the birthday kid is more laid back and usually happy to go along for the sake of family harmony. Child giving birth tends to express preferences more forcefully and has at times cut off family members temporarily if they don't feel they are being treated appropriately.

Newborn visit, of course. If I were the parent hosting the birthday party, I would ENTIRELY UNDERSTAND.

I don’t get the part about gives birth unexpectedly—and asks you to come visit. Is the ask coming during labor? If they’ve already given birth, are they insisting that the visit has to be immediate or on a specific day — that just happens to be the day of the party that you’ve already committed to? I’d go to the party as planned, and visit the newborn the next day. You don’t mention other relationships, so are the siblings and their families going to meet? If so, maybe everyone could meet the newborn after the gathering.

If the very small birthday party has been planned in advance, it would suck to bail — unless there’s some sort of medical emergency with the newborn or the newborn’s mom.

tldr: I would go to the party as planned, and visit the newborn either before or after the planned party.

Of course the history would matter. There are lots of hypothetical possibilities here, so hard to comment usefully without more information — including how well the siblings get along.

I would go to the party then go visit the baby the next day. If the party was early in the day I might drive to the other child after the party.

I'd do the six hours of driving.

Yeah, while new baby is a bigger deal than a birthday, it’s way less time constrained. Go to the party, the next day head to the new baby. Stay a few days and help out however you can, which is usually things like dishes, laundry, making food for mom than actual baby care.

She already missed the actual birth, so unless there’s some specific reason the new mom wanted grandma there that specific day, it’s hard to imagine her getting mad about a next day arrival.

However, I could see the parent of the birthday kid being a bit put out about a non-necessary last minute cancelation. But a reasonable person would get past it with a shrug and a “we’ll miss you!”

Newborn will still be there the next day. Unless there's an actual emergency, I tend to keep my pre-existing plans - I find that this feels the most fair and is the least likely to upset anyone.

Also, I may be reading into things too much, but the child calling and asking you to come on the day of the other grandchild's birthday after being on bad terms for months seems manipulative. Is there any reason you can't see the newborn the following day?

Not sure why on became in ^^

I don’t understand why the visit has to be in the same day as the party. Sounds like the baby was already born? So why does it matter if the grandparent comes to visit in a Monday instead of Saturday?

I'd do both on the same day (unless one of my kids was willing to change the date of the party/visit).

You go to the party and next day to new grandchild. Be kind to your kid or you may never have a chance at a relationship with that new grandchild

A birth is literally once in a lifetime, a birthday is once a year.

Want to run this by the forum to see what you all think of this scenario. Imagine that you are a grandparent planning to visit one of your grandkids for a birthday - the visit was planned in advance, parents have made some preparations for this visit, it's on the child's actual birthday and there's a party/gathering with just the grandkids, their parents, and the grandparent. Small enough that your absence will be noticed by your kid and their spouse, but the birthday kid is young enough that they may not notice.

Your other child gives birth unexpectedly a couple weeks early and asks you to come visit - this falls on the day of the birthday party. You have been somewhat on bad terms with this child for a few months, but not "estranged" per se, just an argument. You wish to reconcile.
Do you go and visit the newborn, stick with birthday plans, or something else? Would be very difficult but not impossible to do both in one day - probably would be 6 hours of driving.

How do you communicate this with whichever child you're not going to see that day?
Both of the grandchildren are young enough that they won't care or remember, but it's more about your relationship with your two kids.
Flipping the scenario, would either child have the right to be put out if the grandparent can't visit, or is it reasonable to chalk it up to awkward timing and everyone lets it go?

How would past patterns of behavior from the grandparent affect your reacting in either child's position (i.e. cancelling past visits on holidays/important days due to circumstance not entirely within the grandparent's control)?

Sorry to be ambiguous to my role in this scenario, I want a completely unbiased reaction - I've tried to be objective.