Satsum can I ask if your MIL is still quite young?
The reason I ask is that I am still only 47 and no sign of menopause yet so could still possibly, maybe conceive another child of my own, and when I first picked up my lovely newborn grandson I felt exactly the same emotions as I did when my own babies were born, that sense of wanting to protect for ever and an almost spiritual love that is hard to explain unless you are a mum yourself, you will know what I mean lol.
I am just wondering if your mil is somehow feeling broody for a baby of her own to love and nurture and if her emotions are somehow taking her back to when her own children were babies, that she temporarily forgets that she is granny and not mummy.
Only a suggestion but I personally see how easy it could be to slip back into the mummy role.
I am, however, fully aware that my DIL is the most important person in the world to little Harry and I will never step on her toes consciously!!