My sister left her son with me to vacation when he was little, and again when he was about 3. The hospital authorization is an excellent suggestion. We have one authorizing me on any occasion since I spend so much time with them. I think it is for any occasion which reminds me I need to check on that.
He was very happy to stay here. It was lots of fun.
You didn't say if your child was being watched at your home or your mothers. Since my nephew was staying here, we ran through all potential danger zones, putting electrical socket protectors, etc. (I already had child proof locks on my cabinets and such for when he was here)
When your child gets older and if you decide to vacation again, (the second time my nephew was 3) ,
we made a vacation scrap book that was his. We put a picture of Mom and Dad in the front waving hello with notes where they were going, a calendar with the dates marked they were coming home, and then the rest was for him to put pictures and drawings in of his vacation with his Aunty! He takes it out occassionally now (he's 6 and likes to reminisce about it.)
Have a wonderful time.