My son was a P/C starting at about age 13 through college. Very difficult and I wouldn't recommend it.
BUT having said that you do need to establish a set of rules if your son is going to do it. --- Use common sense.
Pitching requires "recovery time". This varies between players. Use Pitch counts to determine his use and use days to determine his recovery. For instance, you may set a 90 pitch count as a limit for a pitching outing and 3 days rest. During that three days he may play 1B or be used as a DH but no catching. After 3 days rest he was able to catch OR pitch. My son didn't need a recovery period from catching in order to pitch --- in other words he could catch on Monday and pitch on Tuesday but he couldn't Pitch on Monday and catch on Tuesday.
Now, How do you handle this with the coach??? Depends on you, your son and the coach. When my son was being overused, I established his pitching-catching-recovery rules and discussed one on one with the HS coach and, as I expected, he became irritated. The coach finally agreed and my wife became the pitch counter and everything smoothed out. College was quite different in that the coach never abused his arm.
Fungo