Fritz,
JJ is correct. As you (correctly) pointed out, when the defensive player who is "sharing" the batting order spot with the DH pinch runs (or bats) for him, the DH "role" is terminated for the remainder of the game - on the other hand, the player who was fulfilling that role is not "terminated".
Under FED rules, when a team elects to use the DH, they have 10 "starters" and nine batting order spots. When the defensive player sharing the DH spot plays on offense, the offensive player leaves the game; in effect, he is substituted for with a(nother) "starter". Since he is a starter, he has the privilege of re-entering the game one time. The defensive starter who "enters" on offense has never left the game/been substituted for, so he may still leave the game subsequently and re-enter on more time.
So, in your sitch, we have the DH batting for the pitcher. The pitcher comes in to pinch run for the DH after the DH reaches base. The DH role is now terminated for the remainder of the game. Subsequently, the pitcher who pinch ran has his spot come up in the lineup. The manager chooses to sub the original DH to pinch hit. Perfectly legal. That player has now "used up" his starter's re-entry privilege. He gets on base and the manager has the pitcher pinch run for him. Perfcetly legal. The DH is now done for the remainder of the game and the pitcher has "used up" his re-entry privilege.
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