J.C.
If your daughter isn't coming home with bruises then I would say try to relax a bit. Of course hitting isn't okay, but its perfectly normal at this age. I'm sure Grandma is doing a good job, and your daughter will face aggressive kids no matter where she receives childcare. At least now she is with family, not strangers.
I would try asking Grandma every day when you pick up your daughter, "Did she have any problems with hitting today?" If you do that every time it will show Grandma how serious you believe this is and will open the lines of communication so you can see how she handles it.
The problem is not really the hitting 4 year old, but how your daughter, and her caregiver deal with the situation.