Okay, so from what I'm hearing, this guy is threatened by your success.
Not only that, but he has no respect for your property, and literally wants to "dump" on your earnings. I don't think it makes a difference that you failed to dump trash, it's not about you being messy (you're tired), it's about him being shitty. Either keep trying to please him (it's impossible) or turn the tables.
Look, it's simple. He has a macho mentality, but nothing to show for it. So tell him this:
"I don't care if you are the breadwinner or the homemaker. But I do a full-time job and earn more than you. Then I come home and do the housework. I am the man and the woman in this relationship. Start pulling your weight, or leave. I don't need you trash talking me when I'm the one doing chores, I don't need you cutting me downh, and unless you help out around her I don't need you at all. You don't like the way I do things? Fine, you can do them! Or you can stop bothering me."
You need to really dominate him and emasculate him here, because that sorta thing is no good. Either he will leave, help out, or that will escalate into physical abuse (in which case, call the police). In all cases, you've either improved things or gotten him out of your life. If he helps out, compliment him, and give him a sort of reward. You need to reform this sort of behavior, by training him to look after the house.
I believe that a household needs a breadwinner to earn income, and a homemaker to care for the place and people in it. It doesn't matter who it is though. But you can't have two breadwinners in competition (the rivalry drives a wedge in your marriage, the house and child is neglected, and one person might wind up doing both jobs) nor two homemakers (the household runs short on money). This is why American marriages fail, the women are trying for both roles, and the husband either competes against her, or is a manchild that doesn't uphold his end. Neither one is cool.
As for the dog, it's basically helping him abuse you. Give it to a shelter, and tell them to get it to a better home.
You have a responsibility to your emotional well being. Anyone who tells you that you are worthless and incompetent when you are the breadwinner and the manager of the household, yeah you don't need to listen tohim. In fact, that's what you ought to do, no threats, no ultimatums, just shut him down and ignore him Stop taking him seriously. He's a big child who can't manage alone so he's abusing you hoping you'll be dependent. How do we treat an unruly dog or child with tantrum? We shut them down.