Once a pitcher is removed from the circle because of too many conferences, that pitcher can no longer pitch for the duration of the game. So your coach was not allowed to put the pitcher at third for one pitch, and then bring her back to pitch again, regardless if the other pitcher delivered one pitch or pitched to multiple batters.
As for a new pitcher's requirements, there is no rule that I'm aware of that says she has to complete one batter before she can be removed.
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"Let's face it. Umpiring is not an easy or happy way to make a living. In the abuse they suffer, and the pay they get for it, you see an imbalance that can only be explained by their need to stay close to a game they can't resist." -- Bob Uecker
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