I think, and I mean this with the best of intentions, you're going to have to pull yourself together and take back control.
As a PP said you have some simple aims: fed, teeth, dressed.
Do everything possible the night before. Bags packed, lunch made, cereal and bowls out, coats out etc (I out absolutely everything that I can into the car including my own coat and laptop etc)
Eliminate all screens. Totally unnecessary in the mornings. Ours are much better since we've dropped them. It was awful for two days and then they stopped asking.
Make sure you have a rhythm and routine to the morning and stick to it, so the kids know exactly what's next. Eg, we do cereal, then toast (15 mins), teeth (4 mins), dressing (6 mins), out the door.
If you make a threat, stick to it. Take your child to school once in their PJs and it won't ever happen again.
Eliminate transition points. Eg toothbrushes downstairs, uniform downstairs, hair brushed in the car.
I don't attempt breakfast before they're in school either. I find my day is so much better if I'm less shouty and stressed in the morning.