Feel like we're missing some info here. Get medical note saying he needs to rest arm or let coach be in charge of your kids arm for 4 yrs. if he's such a great coach why does he want your son to throw when it's only practice in Fall? Is he a work through your pain kinda guy?
IMO medical issues r one place where parents may need to do the talking w the coaches. Kids don't always present the facts correctly.
Tough spot between not wanting to cause issues w coach vs keeping your sons arm healthy for the next 4 yrs. good luck-keep us posted.