It's typically harder for a horse to trot slowly than quickly, so slow trotting will build up the muscles more than rushing along will. Also, when they're rushing they're usually on the forehand and not using their rear...has your trainer/friend taught you about getting the horse on the rear yet? This helps immensely, but it's sometimes difficult for an out of shape horse to use their rear properly until the muscles are more built up.
Slow trotting is always helpful though, Sandie and I did a LOT of that when I first got her and she was really out of shape...it's been a year and we're only now really focusing on getting her back on her rear now that she has the muscle toned back end to do it more easily.
"The times when you have seen only one set of footprints in the sand, is when I carried you..."