OP, there have definitely been some real positives today.
It's not going to improve overnight, but if he went back to bed (even after a racket), that's a win. If you got an hour of play without him kicking off, that's a win. If he did less shoving during the walk, kick notwithstanding, that's a win.
If he knows you mean business, this will reduce over time, particularly the waking her in the morning.
Agree with others re TV. If hes allowed 10 mins PlayStation then a programme or two spaced throughout the day won't hurt. Do you have cushions or blankets you can put on the floor? You can place them on the floor and instruct each DC to sit on one (even better if you have different ones that can be exclusively "theirs"). You can use them to control how close they sit to the TV, and control the distance between them (more than an arms length to minimise hitting). Tell them you want them to stay on their cushion to watch tv. At first they will need lots of reminders, so get a cuppa and supervise, but as they both learn they will move less. You can remind DD as much as needed, she's not too young for that sort of reminder, if she went to nursery she would have that sort of reminder. That will help DS to learn that he's not the scapegoat. In time they will be able to be directed "get your cushion/blanket, and when you're sitting nicely we'll put the TV on."
Don't punish if they move, just remind, remind, remind. I can imagine that in DS's mind, he only hits DD because she's blocking his view, if she didn't do that he wouldn't hit her and the TV wouldn't get turned off - so to him it's another thing that is his sister's fault. He's trying to communicate that she's blocking his view, but doesn't have the language, he needs you to tell her. You don't need to use negative language, just "DD/DS, please stay on your cushion." "DS you've been sitting really well, show DD how to do it!" And so on.
If either gets up and wanders away, that's fine as long as they don't block the others view or start throwing things.
I think you've done amazingly in just a day. I really want to hear how the nursery pick up goes tomorrow and how DS reacts to Daddy being there. If this thread fills up overnight please will you start a new one so we can keep trying to support you? 