AFTER READING YOUR SO WHAT HAPPENED:
Mama you'er reply indicates that your have nothing but negatives in your life and household. Your daughter is feeding off your attitude and willingness to cater to "what she will do and not do". So you are a stay at home mom and there's nothing in your town in the way of youth activities, YMCA or church activities? OK, then it is up to you to get your 11 year old in gear and take her out of the house daily, even if its just to walk and talk and get her and the dog some exercise. (Your son should probably go as well).
As for the meal preparation, YES you can just prepare breakfast, lunch and dinner without being a "short order cook". They will eat what your serve or wait until the next meal (with NOTHING in between). I don't think either of your children will starve. I'm am hesitant to ask this, but is your husband as picky as your children and are you catering to him as well?
Nothing is going to change until you take the lead.
Blessings.....
Is there a YMCA in your area? If there is, put her in a few activities each week. I suggest yoga, swimming and perhaps an exercise class. (Yoga and exercise can sometimes help when one is depressed. If you don't have the money for a membership, the Director can/may be able to give you a free six month hardship membership. (They did that for me several years ago when I was unemployed).
If there is no YMCA in your area, check out the youth groups. Some churches have really good programs to w/counselors that may be able to help.
Diet has a lot to do with how we feel, mentally and physically. The weight gain in also a concern, so I would cut down her portions, cut out any soda, sweets, including sugar packed cereals and snacks in between meals. If she want them back, tell her she must eat some salad or veggies with her meals. I would not be taking her to any restaurants if she causes herself to throw-up---that appears to be a control thing.
Most importantly, keep talking to her, even if she isn't talking much. Let her know she is loved and can tell you and dad anything that's troubling her. I agree with speaking to her school counselor and/or some of her teachers. How did/does she do in school?
I would take away the computer, Ipods, phone etc. I would also insist she walk, feed and clean up after her puppy. And as far as the classes, just put her in the car and take her there, you may have to stay with her until you can trust that she is going to participate. She is just 11 and your the mama,
show her who's in control and if she wants more freedom, her life needs to change.
Blessings....