Asking her to pay a second time for the same filling WHICH WAS NOT DONE is double charging. If she paid for the extraction once, they will have a record of it, and if the originaldentist recorded her work it should be clear that the appointment was a disaster and the filing never got done. even ifit had been, when I get dental work done, I "sign up" for a set time and anything needing redone within that time is free.
Plus, any remedial work she needs as a result of the complications of the original extraction are the responsibility of the dentist who did it or the head of the practice. There will be an A&E record of the emergency treatment she received, the cause of it, and the date.
Perhaps the original dentist left abruptly because of the standard of her work (and record keeping) and the practice head is wary of admitting too much responsibility in case your DiL takes it further and sues for recompense for the pain and trauma she received? In fact, given the result of her "treatment" they should be falling over themselves to be nice to her.
I suspect she needs to find a new dentist.