Not sure if it was quite as bad as you seem to be having it but when ds was 18mo it did get pretty hard with his constant demands.
He used to be awful in the a.m. waking screaming like you say, screaming while I tried to get his brekkie and feed the cats, make a cuppa for myself etc. Oh My GOD!
It has calmed down now, he is 21mo, not sure if it was just a small phase that has passed, or he communicates a bit better or we have got better at dealing with him but at least maybe I can give you hope that it passes??
Now dh and I get up together (we used to take it in turns - 5.30am starts!!) so one can keep him busy while the other gets breakfast. He LOVES washing up so we always leave some dishes from the night before to do with the breakfast dishes. That keeps him happy with dh while I shower and dress. Then dh showers while I take him to his room to open curtains/ make bed/ get him dressed. Then we settle down on the sofa to watch In the night garden with a cuppa before everyone has to start getting out the door.
Basically we tag team, if he is 'forgotten' about while dh and I rush about getting ready he gets bored and anxious/ demanding etc.
On days I don't work and am with ds at home then as soon as dh goes out I get out of the house too, to have a coffee, take the train to town, park, supermarket, meet friends. ANYTHING! staying in is a one way ticket to small child induced madness
Ds is also a bit anti-daddy at times (i.e. when I am around) so if I need to get something done the best thing is if dh actually takes him somewhere else where he can't see me. Doesn't have to be outside, even to his room, or - again - washing dishes - will do the trick.