I like our kids getting outside instruction, no doubt. We have 2 rules pertaining to them in season:
1. No pitching lessons in-season. We have a pretty structured pen schedule to keep our kids sharp, and we know the most likely days they'll be throwing in games. If they throw 1 (sometimes 2 ) pens with us, and then possibly appear in a game, there simply isn't a (simple or easy or foolproof) way to safely throw with an instructor. It just increases the chance of injury. And let's be honest, a lot of teenagers suck at communicating, so knowing if or when they threw outside of us is difficult.
2. No missing practice time for private instruction.
We're like Cabbage in that if you're being taught something different we want to know about it. We don't give ultimatums at all, but we like to know the "why" behind what a kid is being taught. Up to the kid ultimately what he does.