There is so, so much that is going unsaid in your post.
Why did you move away from all her friends? You do know that she is grieving the loss of her friendships, right? Can you see that? Did you move because of HER issues, because one of you got a new job, to be closer to family -- why? Is it possible that stress from the move is behind both her and her dad's frustrations?
Why do you have foster children if your own nuclear family is having these issues? Did your husband and daughter have issues between them before the new kids joined the family? Is it possible at all-- though you will not want to see it, I think -- that the presence of the foster kids is changing the dynamic between your husband, your daughter and yourself? Does she feel that they get your attention while she is losing your attention? Please consult very seriously with the foster care program and get counseling through them to determine if your family right now is a family that should be fostering kids. You may need to be strong enough to question whether you should be foster parents while your daughter is still in your home. This may be a temporary blip that will work out, or it could be a problem deep enough to mean you need to stop fostering for a time--it sounds like you need the help of the fostering program and a counselor to find out.
You and your husband MUST get parenting counseling immediately. Please do not say "we can't afford any specialist"! Your city or county health department and/or social services department can link you to free, low-cost or sliding-scale family counseling. Also try your local "women's center" which are advice centers all over the place -- look them up for your area. And have you checked into what your health insurance will cover? You might be surprised, and you might find that many counselors or family therapists will work with you on sliding scale fees or payment plans. If your husband flat-out refuses to go, go by yourself and/or go with your daughter, whichever the counselor or therapist recommends at first. He needs to get out of a rut where his only way to relate to his child is to yell at her and she needs to be able to see him as something other than dad who yells at her. I'm not saying he's the only one at fault -- but he IS the only adult in that screaming match, and it's his role and responsibility to deal with things better if she cannot.
Someone else mentioned below that your family seems very controlling of your daughter and I agree. I would totally drop the food issue for now -- totally. Just keep decent food in the house and do not discuss it; it has become a power struggle because she KNOWS you cannot force her to eat or not eat anything, so simply drop the struggle for now. She may feel she has nothing at all that she gets a say about -- nothing she controls, but she can control this one thing, her eating habits. You have much bigger problems to deal with first -- can you recognize that? I am concerned that maybe you can't see the real issues because you are focused on smaller ones that are really symptoms (what she eats, her schooling) and not the actual problem (she feels she has no control over any aspect of her life; she is coping with sharing her whole world with not one but two foster siblings; she has had to move away from the support of her friends, and much more).
Please get outside help now, this week, today. He too sounds under a lot of stress -- did you move for his job? Does he possibly not like that job, it's not what he expected it to be, he is regretting the change and taking it out in yelling at everyone--? He needs help, you need help and most of all -- your child needs help. And what about the foster kids? Surely they hear all this? Even if dad is sweet with them -- they see that he is not sweet with his own child, and they are feeling all the tension in the household.
One last thing. I know you homeschool but be open to the idea that she might do better and be calmer if you can find a school or some kind of homeschooler co-operative where kids study in groups. That way she can meet other kids in this new area, join some healthy extracurricular activities for interest and fun, and have exposure to other adults (teachers, Girl Scout leaders, coaches, homeschooler parents in a co-op etc.) who are not you or your husband. It all sounds like there is too much togetherness right now and not enough outside activity, independent of the rest of the family, for her. I'd get her into some activities all her own as swiftly as you can--whatever interests her, arts groups, drama or music or a sport or dance lessons or computer programming classes, anything that interests her and that she helps choose, so she feels some control.
But whatever you do, you and your husband need to get third party help to cope with his anger (and the real reasons behind it) and your child's disaffection. He needs to ramp back and not engage and yell, and she possibly needs more to focus on that is not about the new house, the move, catching up on her schoolwork, or her foster siblings.