I think you have identified a number of the problems and just need support. I understand he is injured - so what is he doing about his situation? I hope he is pursuing help, either thru PT or nutrition. If he works until late, and he cannot take dd to school, can he help in the morning with non-strenuous tasks? Can he make lunches, read to the kids, help with breakfast if he's not lifting anything? That would let you get yourself ready.
You have to do dishes, but you could use paper plates once a week just to save your sanity. Call it "picnic night" and have fun with it! You don't have to clean all the time. Let it go. Throw the toys into bins, take a damp rag to wipe down the bathroom, don't make the beds. Make this a gift you give yourself, rather than look at it as "I'm failing, I can't do what I should." Your husband could maybe wipe down the bathroom sink and do a quick dusting of surface level things that don't require bending. Can he pay the bills and organize the grocery list, even if you do the shopping?
The kids are sensing your stress and they see a window of opportunity, probably. You also have less patience and are more tired. The yelling doesn't work, as you know - it's just a natural reaction to frustration. Put the kids in their rooms to play quietly - separate them from each other and from whatever they are getting into. When they are in their rooms, can you read (just don't look around the house for stuff to do!) or put in a short exercise DVD to get you doing something for yourself?
Your stress level may be something the kids pick up on at night, which is why you can't put them down on time. The older child can start to do some of her own nighttime prep - big girl stuff, call it - like put on her jammies and brush her teeth while you read to the little one, then you have your special calm time with the big one. Concentrate on being calm and that will keep the kids from being revved up. Don't think about what else you have to do that night - just concentrate, for 2 nights, on relaxing and having everyone in a state of calm. They may settle down more easily.
Try to get a babysitter for some time on the weekend so you can do something for YOU.
Hang in there!