Ordinary effort and/or the alternative approach for F9 would have been to take a step or two at an angle back and to the foul line, catch it on the one hop, let R3 score for the tying run, and try to throw out R2 at home to prevent the winning run.
Whether the fielder makes a good choice on how to make that play is irrelevant to the scoring. It's solely a question of whether she made a physical error in attempting to catch it. She did not.
Also, regarding single vs. double, did the batter attempt second base? Not sure that's a good idea. There would be the risk of being thrown out before the winning run can score. Unlikely, but not sure I'd be trying that.