Hi C.. My son also has ADHD at 7, and last year was borderline ODD. My cousin's child has had many similar behavior problems, and she got him into a program (he's 10 now) something like the "boot camps" you see on TV. It really worked for him. For a girl, though, that might be really harsh, and she is only seven. Another option is definitely some counseling to help her cope with her anger. Many schools also offer anger management through their school counselors. If you have not had her tested through the school system, it might be a good idea~ they have to do something if you ask for testing, usually within 60 school days. They might find that even if she doesn't have a qualifying learning disability, she would do better with one-on-one classroom time than in a larger classroom all day. Usually, they are in a smaller class for part of the day, and with their larger class the rest of the day.
You might also keep a journal of her outbursts and see if there's a typical pattern, and her teacher could do that as well. Sometimes ODD is worse because of triggers--cold weather=less daylight, certain times of the day, or even watching a particular TV show. My kids watch almost any TV show that is on PBS, Nickelodeon or the Disney channel, and sometimes Cartoon Network, but I find that my son's behavior is noticeably different after he's watched some shows.
Since you do have so little free time, I can understand how you would want to spend every spare minute with your daughter. Unfortunately, when we are stressed out because of the demands in our lives, our kids get stressed too. (I'm going through that a lot with my 9-year-old, she has a LOT of anxiety.) Maybe you could try a girls' day out. My daughter and I went out one day and got haircuts and our nails done. Then we went to lunch and to a movie. It can be more cost-efficient to do it at home, though, rent a DVD, buy a new nail polish and spend the day in. During our day, my daughter confided in me a lot and told me what she was so worried about. I was able to make suggestions that helped her a lot.
I hope this helps. ODD is a hard disorder to overcome. Psychology websites might help. (I learned most of what I know from my psychology classes, and research when my son was close to being diagnosed.) It can be scary, though, and some psychologists say that ODD is a precursor to antisocial personality disorder, but I believe that it can be overcome and never get to that point. You have a LONG time to turn this around. Good luck!