I don't see an issue....I assume your son hadn't thrown a lot of pitches. He likely warmed up a bit in the OF between innings, so it's not like he was coming back in cold. If he never leaves the game it's not re-entry....he can play all 9 positions in one inning if he wants to.
In NFHS, unless it changed, if you start as the pitcher.....then leave the game, you're eligibile to re-enter the game, but I'm pretty sure it can't be as the pitcher. Could be wrong, but I'm thinking that's how it was when my son was in HS