On coping strategies, mine just involves muddling through. I work pt and use lots of childcare.
I appreciate that this is a very personal decision whether or not you want to be in paid employment and use childcare but for me, it saved my sanity.
It also gave the children a break from each other.
I used to co-sleep with my dd and then ds. They frequently would come into the bed with me and play on weekend mornings for an hour. Some people say co-sleeping siblings get along better, which is something I fell into by accident (dd was a very bad sleeper, as was ds).
As for getting dressed in the mornings, over the worst of it, I got dd to sleep in comfy clothes that she could wear to nursery the next day. So problem solved.
If ds starts to seriously tantrum, I put him in the middle of the carpet and let him get on with it, whilst I do housework and things around him. Dd is not allowed to needle him until him calms down. If it gets too loud, I move ds to the bedroom - it is not a timeout because there is no time limit or closed doors, but I make it clear that he is too noisy.
Does your dd go to school. Can you make friends with other parents on your street and take turns to have children over, so that you get a break. It sounds very hard.
You are not alone. Shouting seems to do the trick sometimes, but like you say, what will the neighbours think!