Dollars to doughnuts you have 2 problems and neither is the starter. Put the battery on a charger and check it with either a hydrometer or load test (both available at your local auto parts chain). While its a chargin' inspect and clean all the electrical connections you can get to (some minor dis-assembly required). As for him riding it down a hill and trying to start it (bump start) this takes the starter completely out of the equation so...it aint the starter keepin' it from runnin. You have some basic trouble shooting to do. Spark, fuel, compression checks. Do the clean-up of your connections first. Bet it takes care of your conundrum.
As to your question. Doubt you'll find a rebuild kit but check your local yellow pages for a shop that rebuilds alternators, starters and the like.
As to your question. Doubt you'll find a rebuild kit but check your local yellow pages for a shop that rebuilds alternators, starters and the like.