Its difficult, I really feel how tough your mornings must be at the moment, and its so easy for it to ramp up and everyone just gets more and more worked up. Maybe there are ways to diffuse the situation though. We had somesimilar issues with Dd and Ds at that age. Things we did to get there were having a visual chart and immediate reward on completion. And I would be firm, blunt even, but if it escalated into tantrums I would step away for five minutes, say, 'you know what you need to do next, I'll be back in five minutes to check on you.' And let them have their strop. A lot of the time, when I came back, they would have done what she was supposed to.
On a wall in their room and in the kitchen, we had a chart which showed pictures of getting breakfast, brushing teeth, getting dressed, brushing hair, putting shoes on etc. Once those were done they could play with toys, but not before or during. Anything I found them playing with during getting ready time went on a high shelf to be given back when we were done. And absolutely no screens at all in the morning, they were way too distracting for my kids.
I found the visual chart also took a lot of the fight out of what needed to be done. The chart became the 'enemy' rather than me if that makes sense. Its on the chart so it has to be done next.
I would constantly be prompting 'what's next then?' To get them through the list, and then they had time at the end for playing if they did it.
I also took Dd out the door in pjs once because she was refusing to get dressed. I warned her it would happen, and now they know it will if I have to warn either of them again.
Mine are 5 and 7 now, and I will say I do still have to yell 'shoes!!!! Nowwwwwwww!!!!!' Repeatedly some mornings but on the whole they manage the getting ready process without too much fuss now. The chart is still up on DD's wall though. And i still say, what's next then? To get them moving. Its become habit for them now. And they've added their own bits to the routine, to fit their needs now.
It was a slog at times, and keeping a lid on my own frustration was/is definitely the hardest part. Not something I was always successful at. But parenting is a marathon, not a sprint, it takes time to make change, build good habits, and embed routines. It doesn't happen overnight.