Champagneformyrealfriends what a nasty cow your MIL is 
When my 3rd baby was a few months old AND sleeping though my MIL insisted laid down the law that she was taking my older 2 DSs (4 & 2) to the beach, then it turned out she was keeping them overnight.. what a night!! I couldn't sleep a wink kept imagining all sorts and swore it would never happen again!
She never took any of our DC anywhere again, mind you we've been NC now for years (psycho bitch abandoned her own kids when they were young, then thought she could come in and take over ours especially our oldest).
On the other hand FIL and his wife have never had our kids stay overnight, even though they have a DC the same age. They never offered and we never asked, even though I trust them completely but just simply because we never needed too.
My own DM, FIL or friends stayed with our kids in our own home when I was in labour.
Just because you eventually allow your DD to sleep over at your DMs or DSs it does not mean you have to allow it to happen with your MIL.. just stick to your guns and don't make the same mistake I did that day/night!
Also if they mention again that you have to leave her anyway to go back to work just say that's even more reason to keep her with you at night time 
Just for the record all my DSs have stayed at Beaver/Cub/Scout camps with no problems at all even though DH and I are leaders and do most camps if we're not there they still have no problems staying or at friend's houses for sleepovers!
Enjoy your time with your little DD, time really does go too fast 