One thing we did when my kids were very little and I had one child prone to crazy disobedience is super limit rules. I know it sounds counterintuitive but it worked for us. For a time it was a daily battle of wills. He was a sweet child, but knew how to skirt rules from toddler hood. For example “I wasnt running I was fast skipping, you said no running.” It was exhausting. We made a decision that obedience and respect for mom and dad were the priority. We decided the only reasonable way for us to demand 100% obedience was to be sure we enforced every rule, every time. And followed thru with consequences every time. So for our sanity we had like two rules we enforced without fail. We accepted nothing less. But again, like two rules, so it was doable. It meant my kids ran wild, climbed fur iture, threw balls in the house. But they understood it was only ok at home. Different rules as grandmas, meighbors, church, etc. They had no trouble understanding this. But when I said (or sometimes had to yell over the chaos) “FREEZE,” they immediately froze and waited for the next instruction. Over time more expectations were added and eventually we had a peaceful home. But for a while freeze was their main rule. We picked freeze because it was clear, not intimidating, not emotional, and does not imply someone is in trouble.
I would also second trying some positive attention. Making sure they know you enjoy them. I was always certain to smile warmly at my children when they entered a room, even if I didnt feel it.
And try not to take poor behavior as a personal assault on you. If we can stay calm and treat it as a chance to learn and grow it helps I think. When we get worked up amd frustrated we lend to tension in the home. When our faces are crumpled and our shoulders are locked up they feel it, and then they get all crumpled too. As mamas we set the tone, try to set a peaceful one.
My husband used to tell me “remember you are in charge here, not them.” Its obvious, but when we let them set the mood they take that control.
Take a deep breath, yell “freeze,” smile at them, and then separate them and calmly, sweetly tell them what will happen starting now, and what the consequences are. Post behaviors and consequences (even if it only says “stop and be quiet when mom says freeze or no _____”) on the fridge if necessary. Then follow through every time. Every time. No need to get upset. “Billy mom said freeze and you are still talking, what was that consequence? Oh, no legos today. I bet tomorrow you will remember.” No need for emotion on moms part. They can have their fit, but it wont change anything. Once they figure out you are in control it will get better.
And try to ignore the people that think you are a bad parent for letting your kids jump on the couch (or whatever), they probably have easy, obedient children and have no idea what you are trying to accomplish. One day when your kids are teens they will obey you and respect you and your relationship will be awesome.