Just adding to this superb advice
Check out BIFF for co-parenting (perfect for grey rock) it helps with deescalation with high conflict people.
It means Brief informative Firm Friendly (or friendly firm) it's a Comms tool for written that can really help reduce justification, apologies, excuses. And just cut to the facts with less emotion (I.e. less conflict) they still might be unreasonable but especially with a parenting app court admissable, you will seem child centred, fair, and reasonable. It also takes the emotion out for you following a process and less triggering.
Only ever respond to the action in the email don't get in to the accusations or drama, don't take the bait however much they try and create conflict, back and forth etc
For example.
(Baby name) Is not available on Monday, due to pre-existing plans. (This is brief summary of the issue)
Can you suggest a couple of other options for this week instead? (This is informative about the action needed)
Next time please give me as much notice as possible as I want to make her available to you, but it's not fair to rearrange plans at the last minute. (This is your boundary firm)
Let's get something booked in this week, if the time works we could make this a weekly thing at the same day/time if it's easier to plan for? (This is friendly/helpful).
If there's accusations of controlling/ keeping my child/demanding, the next biff would be.
XX is not available on Monday.
What other times would work his week work for you to see (him/her)?
(Date and time that works), date and time that works)
Let me know if either of these work as XX is free.
Don't engage with the noise just keep it factual. Don't be there on a Monday.
Sometimes they have to learn the boundaries and know you're not going to buckle under the pressure.