It really depends on the organization and type of event. We have been involved with Scout Leagues where it was common for P's to come and go, even during the course of a single game or DH, based on their scheduled innings. Then, there are plenty of other travel organizations who play in more traditional tournaments where it is the norm to stay with the team throughout, but still some exceptions.
With regard to mixing camps and showcases, you really have to start becoming your own law enforcement. Things get really crazy with a P in demand combined with the recruiting efforts of the player and family. You have to learn to plan, monitor and say no. You guys are the only ones who will be keeping track of the big picture... all pitches thrown for travel, at showcases, camps, with instructor and on his own. You have to have firm guidelines in place to avoid overuse. Figure out priorities, commitments, etc., plan things out and stick to the plan. Again, learn to say "NO, that will put him past his pitch count for that period of time".
BTW, multiple short appearances in a single tourney is not wise unless it is truly a closer role (very short), and even then, not more than a couple. He would have to warm up, ramp up and throw game intensity each time and this takes a toll, even though the actual pitch count may be low.