Only you can help her,I am wondering if giving her some food before she starts homework may help her feel better, maybe lay out some healthful food she can snack on she has just left school its hard to come home and start again , maybe a short respite before hand .I see you have a one year old and yes its hard to watch her and help the older child but possibly it would be a good idea to make the time some to be able to just focus on her, she may be feeling left out and it exhibits itself by her acting out.Beating and shouting only feeds into the frenzy,getting emotional and out of control doesn't help, and I know its not easy .. so maybe work on that as your own task.Make sure that the only food you keep in are healthful snacks and maybe some treats ..Children of this age often go through a picky stage of eating . ,maybe just let her get on with it as long as its adequate for health.good luck to you