Hmmm...if he's complaining that the .357 "hurts his hands", you will definitely not ease the problem by letting him handle a .44. At 13, he's growing like wildfire, and his bones, tendons and other "parts" are not settled into place. Frankly, I'd be a bit concerned that too much recoil at that age would induce problems further down the line, like when he's 45 and early arthritis or other ailments start to set in.
I don't have a problem with .357 or .44 recoil, even with the stiffer loads, but I didn't start shooting them until I was almost 30. I'm 53 now. The horse is out of the barn with the .357 as far as your son is concerned, but I think I might try to back him off a little for a few years, maybe switch him to .38's or 9mm's. Also, make sure that his grip is correct, and he's not trying to control the recoil with just one wrist and forearm. Just my 2 cents...