While I'm not a millitary mother, my sister is int he Army. She too went in at 19, and the first month was the hardest.
She had plently of experience in NJROTC, but the cultral shock and complete change of life style can be over whelming. No free time, no loved ones, it can be really tough. It can also be very rewarding! The achevements she will make after this inital trainging will be wonderful! My sister just came home after spending her year in Iraq, and she's stronger, physically and mentally!
It is tought, for both of you, but continued encouragement from you and the rest of your family is what she needs right now. This is the first really big step "out of the nest" and it is hard, she's responsible for all of her actions now, and doesn't have you there every moment for advice. But it will be better for her in the end. The millitary is the best thing, as far as I am concerned, to help young adults transition from the teenage years to the all important desicion making years of a young adult's life.
Just my two cents... I wish you both the best of luck!