Oh honey! Hugs hugs hugs and more hugs! It sounds like you are having one hell of a day.
I am going to speak freely here (type freely - lol) and I hope I don't offend you with anything I say. I am just trying to be helpful. I have two little boys too, so I know how energetic they can be.
First, I have times when I feel permissive too. Then, I have times when I feel too strict, so I don't really know where I fall. Nobody is a perfect parent though. Some parents are more permissive and it can work. You can still raise good kids. Some kids are more wild than others and the parent has to find ways to work with that.
One thing I am big on in my house is taking responsibility for one's actions. It kind of falls under the natural consequences thinking, but I think it is important for kids to understand that their actions have consequences. Sometimes taking responsibility is simply admitting that you did something and apologizing. Sometimes it goes beyond that to helping to rectify a situation.
Also, it sounds like your boys' screaming and crying really gets to you. Don't let them see that it rattles you. They KNOW they are getting to you. For intance, it was NOT your fault that your ds got cut on the tile. You couldn't foresee that, yet you told him you were sorry. Sorry for what? You didn't do it. I would maybe say "that looks like it hurts" or something like that so you are showing him empathy, but saying you are sorry implies to your child that you are responsible for it. He thinks - "how dare you make me clean up my mess" and screams to make you feel bad, then he is off the hook. Trust me, these kids are SMART and know they are getting to you.
Also with your boys climbing on the back of the couch, my dh and I discovered that we can't just tell our kids to stop something, especially the toddler, we need to physically redirect him. He simply does not listen to all the "stop climbing on the couch" no matter how many times we say it. We have to remove him, tell him "we don't climb on the couch" and if he gets up there again, we remove him again. 100 times if we have to.
If you are going to lay down some ground rules, I would start small. Have maybe 3 absolute, must follow rules that you redirect them from EACH and EVERY time they break them. Praise the heck out of them when they have a stretch of time where they have followed those three rules without error. Maybe start with some simple things, like they cannot touch the tools. Of course, the tools are kept way out of reach, so they will be able to follow this rule. Have one other easy to follow one and one that is maybe a little tougher. Tell them ahead of time what the consequences are for each thing. "If you touch my hammer, I will have you clean it and put it away." Whatever you decide on. Then, every time they break a rule, do exactly what you said you were going to do. Some kids need things spelled out. How could they know that they couldn't touch the hammer if you never told them?
They will cry and scream and find all kinds of ways to make you feel bad, but I bet that after a few weeks, things will calm down. Then you can introduce a few more age appropriate house rules. I don't see anything wrong with having 5-10 important house rules for your kids to follow. Kids NEED structure. They behave better with structure and rules. I'm not talking about a really super strict environment. Just a loose structure, so that they know what to expect. They know there are consequences to their actions, etc.
When I have things that I really need to get done and my boys are not letting me, I give them a small job to do. Even the toddler. He likes to swiffer the floor or "fold" towels. Anything. I find that it makes them feel included and helpful. My six year old really gets a sense of acomplishment from it. He is good at so many things and I think this is because we had him helping us from an early age. He helped me paint the computer room last week. He is quite good at it. My toddler "helped" too, by using a very lightly loaded paint brush. So try to give your kids things to do so they can have accomplishments and stuff to feel really proud of. Then, you can talk about how good of a painter ds is the next time you are on the phone with someone, where he can overhear you, of course - lol!
Maybe you do all of this stuff or maybe it doesn't appeal to you or doesn't fit in with your personality. The important thing is to find what works for you and your family and be consistent!