Rule 5.11 - The designated hitter can be moved to a fielding position during the game. If the DH is moved to another position, his team forfeits the role of designated hitter, and the pitcher or another player (the latter possible only in case of a multiple substitution) would bat in the spot of the position player replaced by the former DH.
You have no DH for the remainder of the game. The position is forfeited. That's the game working as it should. That's baseball, sorry!
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