In our area, $25-30 per day is very common. Use that as a starting point. Also, consider having food around that you know your mom would love, so she can just eat lunch and snacks at your house, rather than have to bring stuff from home. It's a small but nice gesture.
On a side note, I'd highly recommend discussing with mom (and maybe even writing out) a general typical daily schedule. Nothing too detailed, but something like "8am wake up, 9am play time, 10am snack, 11am reading books, 12pm lunch, 1 pm nap, 3 pm wake up and snack, 4 pm play until we get home). It will give her an idea of what to do during the day. Maybe even offer to pay for a museum pass or local park pass so that when mom is over, she can take your child somewhere special and not have to pay out of her own pocket. Maybe suggest one day to stay home and one day to go out to do something. Plan ahead and keep things positive so that you're all on the same page!