We spent one very rainy ( and actually our ONLY all day rainy day in 14 trips) in MGM. Most of it is indoors.. and the shows last long and you are sitting down.
Indiana Jones is 30 minutes
Beauty & the Beast is 20 minutes
Little Mermaid 15 minutes
Playhouse Disney has to be about 15-20 minutes
Backlot tour says it's 35 minutes
Great Movie Ride is 22 minutes
Muppets 3-d is 25 minutes including preshow
then, if its still raining, you can take the boat to Epcot, and land by France and stay in the countries!