Yes how about you focus on her positive side and praise her when you see her doing something good , children respond to care affection and praise,you say you love her that is great, so overlook the slammed door ,do not make an issue of the small stuff,,is sounds as if she has had a lot going on in her life . As for eating ask her to come shopping and let her choose the foods she likes, and ask her to help you cook them, when she is at the table let her be in control and back off when she isnt hungry.she will eat so less worry from you.