Grandma went shopping for a few hours - not reason enough to alternate weeks in the summer.
A 13 year old is perfectly capable of keeping an eye on a 2 year old for a few hours. The children in my household are 17, 14, 14, 11, 8, 8, and 7. They stay home alone together in varying combinations, and for varying lengths of time. No one has died, burned the house down, or been maimed yet. And only one of them went to preschool (the horror)!
Why did you need to come into Mom's house, when Mom wasn't home, and get a coat for your 2 year old IN THE SUMMER?
Stay out of Mom's house. Acknowledge that what Mom chooses to do on Mom's time - unless imminently dangerous to the child - is Mom's business, not yours. Be a good parent on YOUR court ordered time, and accept that Mom is a good parent on hers.