Sounds like your runner in the first game was legal. Once the pitcher has possesion of the ball in the pitcher's circle, the runners can stop once, then commit to the base they're adavancing towards or retreat to the one they came from. If they just stand there, or if they stop again, they should be called out. This is called the Look Back Rule (LBR).
If the pitcher in turn makes a play on the runner (which in your case she did by throwing to the SS), the runner is released from the LBR and may do whatever she wishes till the pitcher again has the ball in the circle, when the LBR starts over again.
Hope this helps.
-Josh
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