I wonder too if there's more going on here --- she sounds seriously overwhelmed. If she can't sit still at home either, I'm wondering if she unmet sensory needs or yes, ADHD. Impulse control is indeed an issue with kids with sensory needs and ADHD.
I'd ask that the school counselor be brought and and share what you've shared here: "We're out of our league and don't know what to do next."
Personally, I wouldn't have downplayed the losing recess. I wouldn't have made a big deal out of it because I think it makes no sense to keep kids who've got too much energy in so they can't burn up their energy. We have a very similar system at our school (only it's called the Thinking Room). I think ds will get through elementary school without getting sent, but I'm sure dd will go at least once. Dd and I actually talked about the Thinking Room once and I asked her what she thought kids learned from it. Her answer? "Not much. I think kids who need to go to the Thinking Room need extra recess, not recess taken away." That's one wise 7 year old. But since this is an ongoing issue for your daughter, I think more does need to be talked about. Can she articulate what might help her?
Do you think the school would allow her to sit on a balance ball or seat cushion like this: http://shoponline.pfot.com/seatcushions.htm -- they are a little wobbly and actually help kids like your dd pay attention better. Because they have to focus on their core muscles to be able to sit, their need to move is taken care of and their minds can focus.
Could the teacher and your daughter work out a system where your daughter has someplace different to put her homework where she can't try to sneak it? (I can totally see my daughter doing this because she hates homework, and she doesn't like discussions that she's not in charge of!)
As for the hitting/punching what have you -- no clue there. It sounds to me like it's very uncharacteristic behavior for her, and so I wonder if there's something else going on -- is she stressed? is there some bullying going on? How are her social skills when compared with her peers? Third and fourth grade girls can be very mean -- it's really the start of their socialization, and they're not very subtle about their power plays! (It's one major reason I didn't push for our dd to skip a grade, when intellectually, she could have. She's got a late May bday and is already one of the youngest in the class. Her social skills are on the low end of typical for kids her age. You add that + her young age, and it can spell a social and emotional disaster.)