I do think you sound a little bit overwhelmed Macfee. Personally I think when you are feeling stressed it is harder to stay calm and be patient. If you are working full time as well this can not be easy. I repeat everything at least 5 times before anything gets done, I expect to now, because that is just how it is with children of this age. I would have a look at your life and see what you can reduce, how you can have more time to enjoy your ds and not feel so harassed and stressed that you are resorting to shouting.
I am a calm(ish) parent after a brutal childhood I knew I had to do things differently, and some of the ways I keep calm even when pushed to my very limit are:
I listen to classical music almost all of the time, it definitely helps all of us feel much more peaceful and calm
I massage dds at the end of the day, it is stress relieving for me and they can not get in and out of the bath quick enough for 'spa time'
When I am on repeat requesting mode ~ I count with the repeats to keep me calm
I remember what it was like to be shouted at all of the time by my father, and really resist becoming the same person. Every time I feel I am losing my patience I picture me being composed and the mother I want to be, and then keep going with the calm voice. It is a habit like any other.
When I am getting angry I lower my voice, and do the opposite of what I feel like doing. It makes me FEEL more in control even though I don't feel it inside
If you are putting on coats or something, make a joke of it, tickle them into submission.
I always race my dd to see who can finish first putting on shoes, hats etc that often works
I remind myself I am in control. And I am.
I remind myself they are only small and do not always mean to be difficult, they are tired, may not want to go to school, feel pressure from other places etc.
I make up a million things to see outside to encourage them through the door, the birds, the sky lit up, a shooting star, the moon. Given a reason to put on a coat is half the battle.
Lastly last year, I resorted to printed pictures on the door, and just pointed. No need for a voice and then my dd started checking her pictures to see how far she had come. She got rewards for doing it all by herself.
I always leave plenty of time to get the children ready. When I am rushed it is always harder to stay calm and cheerful.
I have a silent pact with myself that I will never ever shout. Never. Never. If you say it often enough you will be amazed at how it works.
I do not know all the answers to this, far from it, but I hope some of the techniques I have acquired over the years with my children will help you. Good luck!