Great action plan! I definitely agree you need to be either calm or on time! Letting that go will help. If work are difficult, don’t forget you are a grown woman. You can tell them you expect to be late for the next week/ day etc. whilst you’re juggling the kids. No need to apologise, it is what it is.
If you can get up that bit earlier just to have time for yourself, that’s helpful too.
Identify any other triggers, and let that go too. Do they need a morning bath? Anything that can go, scrap it. Easy meals, just for now.
Then plan some fun activities to do. Stick an easy meal on for tea and play board games/cards/music have dance offs and simply muck about with the kids.
One of my triggers is tidying, so if that’s an issue, slow the housework and live in a mess for a while. Care less about all that stuff and focus on love and fun until you have the eldest taking more responsibility. She’s likely playing up because she wants to eat breakfast with you, get dressed with you, have fun with you. So just go for it. Middle child will be the same, so if they argue over games, they each get to pick one and you have to be present. Just until they start doing it on their own. Hide and seek etc. works a treat if you start them al playing, then leave halfway through to get breakfast ready or clean the kitchen.
Also, have bowls, cereal, milk etc. laid out so they can help themselves. Again, don’t stress about mess or how much they eat.
Also to say I’m sorry you had a crap relationship and childhood. It sucks, but you are out of both of those now. You are already winning and you are self aware enough to move forward. It’s going to be okay! And if you do end up shouting, give yourself a break and a mental hug 🤗