i think you are overwhelmed but none of your problems on their own are insurmountable, for sure.
have a go at choosing an important topic (say one that gives you a lot of stress or takes up your time) and work out a strategy then STICK TO IT every single time
for example, going in rooms without permission. if any of the kids ever find this annoying then a rule is needed, even if the child who is refusing entry is being a pain, a clear all round rule makes it easy for you to manage
RULE From now on no child is allowed to enter anyone elses bedroom for any reason whatsoever without permission from the the room owner or a parent, there are no exceptions to this rule.
CONSEQUENCE Anyone who does this will have to stand in the corner facing the front door for (say) 10 minutes for the first offence (make fixed times, but they will be different for each child). Each time it happens in the same day the time will be doubled (ie for this child second offence 20 minutes, then 40 minutes, then 1hr 20 minutes)
You have 3 kids, I can GUARANTEE that if you do this for 3 days they wont be doing it any longer. in fact, after the first poor kid has been there on level 3 or 4 you will find that the others dont even bother trying it.
have a go - maybe post up the most annoying or disturbing problem you are having and see if posters can help you make a plan