This question pertains to High School age kids. And, it's tournaments where you have 3 games of pool play over a one or two day period - to determine seedings for tournament play on day following the end of pool play.
I've seen the catching situation here go down a couple of ways.
Team 1:
The best catcher on the team will catch all of the first game. And, the secondary catcher will catch all of the second game. For the third game, on the next day, it depends. If it's a must win to get seeding, you go back to your #1 catcher for the whole game for the win. If the game has no consequence, then you have your two catchers split the game. Or, if you have a third catcher, then he catches most or all of the game.
Team 2:
Catchers split all the games, all of the time. If you have two, they get 3 or 4 innings each game. If you have 3 catchers, it's a rotation for all of pool play were you get 3 innings on and then the next 6 innings off.
Personally, I see the merits of each method. And, it's hard for me to say which is right or wrong.
My catcher said he prefers catching a whole game at a time. How about your son? What's your thoughts on it?
For the record, when not playing, in both situations, all catchers are full time batters in the lineup. No one is splitting ABs. And, typically, they will be playing another position, at least half of the time, when not catching in the game.