Think only about the batting order. Positions in the field are irrelevant. A team can bat 10 players if they wish, any 9 of which can play the field at any time. The batting order doesn't change and once again, where they play in the field doesn't matter. The one player in the batting order who did not play the field in the first inning can play the field in the second inning (or later in the first inning or any other time).
Obviously, one of the players not in the batting order can substitute for one who is. So, for example, if Jones was the lead-off hitter, Smith can take his place and bat first in the batting order. Smith can play the field or be the EH but Jones gets to sit on the bench. However, once per game, a STARTING PLAYER, like Jones can re-enter the game. But he must bat in the same postition in the batting order as he did previously. So if Jones gets re-entered, he must bat in postiion number 1. This means that Smith must leave the game and return to the bench and Smith is done for the game.
If Johnson is now brought in to replace Jones, Jones is done for the game because he has re-entered already and he can only do so one time.
In NY Travel Baseball, a starter can re-enter even if he was the starting pitcher. AND! He can return to pitching provided that he was not removed on the second visit in an inning. In that case he would be ineligible to pitch because of the rules about visits to the mound.