I have no problem with inning rules instead of pitch count especially for baseball. In your case the rules don't make any sense. However, I would read the rules that if the game ends your innings end. So your pitcher needs to sit out the first 3 innings of next game.
So if pitcher A started the game and went 4 innings, pitcher B came in for 3 innings to finish the game. If you only have the 2 pitchers, who starts the next game? Pitcher A hasn't sat out 4 innings yet and pitcher B has to sit the next 3 innings.
Seems you'd be better off with a 2 game limit of 7 innings. Pitcher A went 4 in this game she can do 3 next game...