Not all umpires are afraid of dealing with a scorebook.
This play could be scored as a SAC/FC for the batter. That's because the runner actually made it to second base before the throw. In essence, the batter did her job. The batter is not charged with an at bat in this situation.
Regarding the runner being out at second... Consider a batter trying to stretch a hit into a double. She slides and beats the throw but her momentum carries her past the bag. Credit her with a double and the out recorded outfielder to infielder. The outfielder is credited with an assist, just as if the runner had proceeded past second base, got caught in a rundown, and was eventually put out.