I feel for you OP, my MIL is terrible at this with my DD. She does the 'sharing secrets' thing and always refers to DD as 'Granny's girl'. Her worst ones to DD (age 2) have been;
"Don't worry baby, when mummy and daddy get divorced you will come and live with me, we will have so much fun" (have a very happy marriage, never even thought of divorce and even if it did happen, I don't think so!)
"If mummy and daddy ever say you can't have something, just tell granny and I will make sure you get it"
and my favorite...
"Auntie (MIL's daughter) would be the best mummy for you, you wait when you come to live with us she can take care of you"!!!
I love my DD to bits but the way my MIL talks you would think I was the worst mother ever! Mind you she did think I was bad to forbid her from feeding DD any of her coffee (when she tried it DD was 6 months old!) but that's another story.
FWIW I had a great relationship with MIL before my daughter was born but now I can't stand her. She does live abroad (we skype twice a week) and is her first granddaughter (my SIL has all boys), I know she probably just wants to make sure she has a good relationship with her but think the way she is going is so evil 
I am glad (in a way) it is not just me who has to put up with this rubbish!