Every state is different, but i can see where it changed from a voluntary term (her giving notice) to an employer termination (you asking her to stay until you decided you no longer needed her). So by her agreeing to stay and you finding a replacement while still holding on to her, you might have shot your employer in the foot as it comes to unemployment payments. In the final analysis, you were the one who made the decision on when she would leave, i.e. to the employer's benefit. I know that doesn't sound correct, but I suspect that is the state's thinking. While you protected your employer in one way, by not having an open position, it costs them in another way. You might consider in the future how much notice you really need becuase it sounds like it only took a few days to replace her.
I know in my state, the employer can accept the notice within a 2 week period and not be on the hook for UI benefits. Anything beyond that, the employee woudl get at least UI benefits (after the 1 week waiting period) until they started the new job. If they leave the new job thru no fault of their own and we are in the lookback period, she would get benefits but maybe we could appeal it being charged against us.
That said, if she has new employment, I doubt she will be on unemployment very long. and if you know where she is going to work, I would suggest passing that information on to the DSE.
I wish I had better advice for you.