Hi,
I agree totally with jasmine1988 comments.
If your daughters periods ceased because she was underweight then they will return if she maintains a healthy BMI/correct nutrition balance.
However, this won't happen overnight - it may be several months after she has reached and mainted her weight before her menstrual cycles begin again, and it may take a few months more for them to then become regular/as they were before they stopped.
She probably won't need to take birthcontrol pills for this to happen (although if she is sexually active it might be good to take then anyway).
Please don't put extra pressure on your daughter, it sounds as though she already puts enough pressure on herself - as jasmine said - she needs your support and reassurance, deadlines and doctors appointments will only be fruitful if it is her decision as well as yours to seek help and advice.
Best of luck to you both.
Cessation of periods are caused by
Stress, which she is probably undergoing in school, and also at her summer job
Poor nutrition, which is likely because she's trying to maintain her weight
Over exercising
Hormonal imbalance
Thyroid gland disorders
You might need to keep a close watch on her, and making sure she eats foods with high vitamin levels, and less of fatty foods.
Make sure she gets enough rest, and you might need to sound more reasurring, so that if there are some issues that are disturbing her, she definitely would find it easy confding in you
Take care.