My MIL (in Ireland) booked flights to be visiting us (in Scotland) for a week before and a week after my due date with dd1 - then told us.
Dh just went ballistic - told her she had no right to assume, that she might miss the baby if she did that, and to his eternal credit, told her we wanted just us there for a few days and then I wanted my family to visit. As we lived on a Hebridean island when dd1 was born, it was not possible just to pop in for a couple of hours (thank goodness!).
MIL took this very badly, we didn't love her, she wasn't really part of the family, she was being excluded - dh just kept repeating that we wanted the first few days to ourselves, over and over.
She had to take several days off work to get over the "rejection" and then found she had booked non-refundable, non-transferrable flights, which did make me laugh a bit - shoudl have asked before she did it, eh?
She's now a fantastic granny most of the time, but often does try to muscle in a bit - gives bigger/extra presents, has more exciting outings when the kids visit her, still sometimes won't take no for an answer, whereas my parents are much more likely to do it our way and take their lead form us (we're not local to them, either).
It is the No1 granny aspiration I think. Some are happy just to be granny, others can't bear the thought of there being more than one granny!