I can only sympathise with you about your awful dentist-- it has been worth every penny to see our lovely dentist privately.
However, I can reassure you and D with the orthodontist treatment. My OD (now 16) had 4 teeth out (she is very lacking in confidence and a complete coward), but the dentist was so good with her that she was actually looking forward to having the 2nd pair out , for the sympathy and the day off school.
She then had top and bottom braces fitted-- lots of paracetamol, icecream and sympathy needed, but visible movement seen within a few days (the pain always seems to tie in with noticeable shifting)
The whole process has dragged on for 2 years, last appt a few days ago, still needs a retainer, but beautiful straight teeth now.
To reassure you even more, I had a brace when I was 26!