You guys REALLY need to do some research into kids pitching and throwing. The #1 cause for injury is overuse whether it be from pitching, throwing, throwing from catcher position or any position. The injuries don't show up when they are 9 or 10 or 11 they show up when they are 16, 17 and 18 playing in the HS team and those 16, 17 and 18 year old kids who are getting rotator cuff surgery, TJ surgery, etc.., NEVER knew the damage they did to themselves at 9, 10, 11, 12 etc..! There is a wealth of information available on the internet pertaining to this stuff and ANY parent whose kid plays baseball OWES it to the kid to educate themseslves about this stuff. Under NO circumstances would I ever allow ANY 10 year old I had influence over to pitch 50 pitches 3 times a week. It simply isn't worth it. If he is a good pitcher teach him proper mechanics and let him pitch BUT DO NOT UNDER ANY CIRCUMSTANCES allow hime to be overused. If my 10 year old were going to pitch twice a week I would not allow him to exceed 35 pitches in the first outing and his pitch count would be limited to 50 in the 2nd. If he went over 35 in the 1st outing he would NOT pitch in the 2nd without 5 full days of rest. If you realy believe the kid has a chance to be a pitcher in HS why in the world would you take the risk of causing injuries that won't be realized until he is a teen at 10 years old? Playing catch or a good long toss session or two between outings will help strengthen the arm and aid in his performance as he grows older but ALL repetitive overhand throwing motions can and will cause injury especially in young undeveloped growth plates!
Just my honest Opinion!
JM