Just by math, it's 18 divided by 3. So, I would say that you would hope that each catcher catches 6 innings each over the 2 games.
But, how you do it is the question. You really can't have each one catch 3 innings in each game because then they're probably only getting 2 or 3 at bats in the entire showcase.
But, if you have one catch 6 innings in one game and the other 6 innings in the other - and then use the 3rd to catch the last 3 innings in both games, then one kid still gets the short straw.
Of course, DHing could help with the ABs but there's 9 other position players on the roster that need ABs over the two games as well. So, there's 2 non-catchers every inning also grabbing pine.
In a week, I will have the answer but curious on what you would do to be fair. Or, maybe fair isn't in play here?