These are lessons to be learned from. And I'm not going to dump on you for it either.
Suggestions: the humidifier NEEDS to be up where your children cannot reach it, nor pull it down by the cord. Ours is a cold-air one, and even without the heater, my son caused trouble with it, dropping bark and soil from my rubber tree into the holes in the top. (my husband now knows how to completely disassemble and clean it, so we've also acquired a new skill). They can also pull out the water container and rub the ball plug on the floor to make a huge mess. (This happened when my husband left that component upstairs as he was taking the other part downstairs to be cleaned. So you aren't the only one...)
As far as bathtime and busy kids, sometimes you are going to need to put one or the other in a contained space. This is when the pack-n-play/portacrib/high chair come in handy. Strap them in for safety, of course. I found that my son did very well in the stroller with a few toys when I needed to have the oven door open, or if he was in mischief mode and I needed to use the bathroom or take a shower. I tried not to make it a punishment, but just "I need you to be here right now, sweetie" and went about my business. This also worked well outside too, when work needed to be done and he wasn't staying away from the street.
And the next time your son scalds his arm (if ever again)-- don't worry about the diaper. You need to get the little guy's arm under cold water immediately, or a deeper burn could take place. If you haven't had any first aid classes, please consider them. Scalded arm always trumps poop.
Sorry, sounds like a rough time. Hope you all get well soon!