People seem to have missed the part in the post where the OP stated that for the MIL to see the baby would involve the OP or her DP having to drive thereto either pick her up or drop her off. So this implies that the mil doesn’t drive.
So not only is she making demands that she needs to see the baby at a certain time in a certain place, but she expects the baby’s parents to facilitate this by driving there to drop off the baby, and presumably to pick her up again, presumably at the time of the mil’s choosing.
And this i a woman who, when told no by a different sibling, stopped speaking to them for two years. That alone would make me say no.
As for needing to be alone with the grandchild to build a bond, what a load of bollocks. I never left my DS with my MIL because she didn’t live locally and wasn’t intrusive anyway. My DC grew up having a perfectly lovely bond with the GP’s. Similarly my ex’s DC only ever saw the IL’s maybe every three/four months due to distance, and in lockdown they didn’t see them for a year and the youngest was only three. And they have a perfectly lovely bond.
I’m afraid that if she’d thrown a hissy fit like that and started saying things like “she’s our bloody grandchild,” I would have responded “actually, she’s not.” Because actually, she isn’t this child’s grandmother, she’s only a stepparent. And while that shouldn’t have to count for anything, if she made those kinds of demands and acted in the way she did it bloody would.