With regards to your sister in law, I’d recommend contacting Ba asap to let them know about the issue. They might allow a change of date.

with regards to anyone else in similar situations checking this thread in the future, I’d very strongly advise anyone with similar or other potentially problematic circumstances from only applying for an Esta a month before a scheduled flight. I don’t mean to add to her plight, and I’m not saying the world is fair, but this is unrealistic. It’s best to plan for the worst case scenario and that means l acing several months before departure to ensure Esta/visa issues can be resolved if necessary.