E.S.
It was exhausting just reading your post...wow! I encourage you to realize most resistance from kids comes as instinct. ( It is a protective mechanism...to protect kids from being influenced by those people the child is not emtionally attached to...usually we think of strangers. Unfortunately though, situations arise in which resistence to parents or other caregivers can occur.) But understand that they really are not in charge of their emotions, reactions etc. (Esp at this age.) It is our job as adults, to try not to "trigger" resistance (also called "counterwill" by Otto rank and Gordon Neufeld). Those that look like masters at handling kids have this skill. Or they have the skill to dodge counterwill when it does crop up.
Note : there are situations where the adult has to trigger counterwill and let the child experience defeat. The adult has to "win" for safety, sanity reasons etc. I guess here is where you have to prioritize to what you can do with the time/energy you have.
To make it easier: you offer the kiddos choices (2 is good) that you can live with, after you have had a good interaction with them, to get their positive attention. (Warm fuzzy bonding feeling...I love my mommy...I know she loves me, she is in control, and we are safe etc etc) One choice feels coercive...two looks really great.
Let these kids be a part of figuring out solutions for simple problems if possible. Automatic buy in...and cooperation should follow.
Model "cooling off"..time yourself out if you are getting to the point of yelling. (we have all done it) Kids may laugh, but inside they may actually be quite disturbed or frightened by parents yelling. (I think my daughter does this too..laughed when I tried spanking too...I gave up on that fast)
A parent who can calmly do discipline is much less threatening. (Ergo Love and Logic's .."wow, what a bummer you did that, now we can't do this or that. Maybe next time you will make a different choice." (message - you are not bad, your choice was not so good...but it can be better next time!)
Try to leave on a positive note..."I'll see you after you finsh putting that away." Kids know mom still loves/accepts them..set up for a more positive interaction next round.
Two's are tough...more strategies like Love and Logic will work better as they age...in the meantime, I'd just try to enlist their cooperation without bribery (except maybe privilages to help you do something you want them too..."do you think you are big enough to ....blah blah??") They sound so active, just trying to chanel the energy to something safe is a score for you!