L.A.
I have fallen asleep holding my infant, but I am up with him all night and exhausted all day!
But if my mil or anyone else who was just watching him for a couple hours alone fell asleep, I wouldn't like it. My fil falls asleep while holding my baby too, but we are usually right there... babies are like little relaxing heaters, that makes people who love them all relaxed and cozy.
But, it would be easy for the baby to accidentally be dropped or roll on the floor, perhaps suffocated, or choked if it is during a feeding. She would feel terrible if that happened too, I am sure.
I wouldn't comfront her until it came up. If she says she would like to babysit, I would just say, "well, I know how tiring it can be, and I know you get tired and have fallen asleep holding him, so I would prefer only him be watched by someone who will remain alert and attentive the entire time."
But make your husband say it, of course. It will be awkward (I have done WAY worse), but everyone will get over it.
On another note, my mil has pretty bad health problems, so I always gauge her level of pain and tolerance to see if she will be fitting that day to watch him. But she will also tell us if she is able to or not at a particular time. So, if you can open up that communication with her, maybe she will open up about her sleeping issue as well, as that could be a health problem. Maybe you voicing your concern over it in a loving way, may help her decide to take action.