First have a plan and communicate that plan to the players. Then stick with it. If for some reason you change your plan, communicate that to your players. With proper communication, most players will buy in. And make sure they know which games they will play in case Grandma wants to come.
I have seen a few things work. Splitting time 50/50 can work. Would even allow the non-playing player to skip a game if needed. If a kid is going to pitch, treat him like a pitcher only for that day. Also, depending on your rule set, use of the pinch runner, pinch hitter, etc. can be effective. We played a HS team this year who had a big roster. The guy managed to get 15 players into the game at some point (not including pitchers). Everyone of his players was ready to go because they knew at any minute they could be called on.