My MIL had 20 years practice being a MIL before I married her son.
DH is her precious baby and will often be found snuggled up in bed with her or having cuddles on the couch.
She's never intruded in our relationship and I know DH is an excellent buffer.
DHs cousin doesn't like how her MIL treats her kids differently from her daughters kids, but I think generally a grandmothers relationship with her daughters kids is easier as she has the freedom you get with your own kids, I'd be very annoyed if MIL took my kids without asking, but not so much if my mother did. It's a different relationship.