know it's not my call but I can't help but wish he'd take this time to get his spiritual self right.
How is he going to get himself right if you're not right? Remember, God says the unbelieving spouse is sanctified by the believer.
Now you let him back into the house, that takes responsibility off him and puts it back on you. I hate to say it, but you are enabling him to keep on the same track. He wouldn't have returned my house until ALL had been worked out and I had proof positive that he was ready to be a husband. At this point, ya'll barely have a relationship, much less a marriage. He's going to continue to be a deadbeat until he runs into a consequence that make him think seriously about what he is doing. God can't convict a person who has no reason to repent.
He's not forgetting that you are a woman. At this point he still doesn't care. You are allowing both he and you to fall back into the same patterns you just drug yourself out of. And if he hadn't of left, you wouldn't have fought him. You were stuck in the rut with a better the devil you know than the one you don't attitude and you are still half in that rut. This is from a lack of faith in God, on your part, that He will meet all your needs.
Why are you still arguing with him? He broke your marriage. It's not up to him to argue with you at this point. You need to tell him that he has yet to prove that he can be a true husband to you and until he does there can be no marriage and no arguement. Right now, all you have is a piece of paper.
You need to consider things from his point of view and make certain that you know everything there is to know about your and his finances. You might not can see why he wants you in a higher paying career, but I bet he has a reason and it may not be a bigger house. Men have all sorts of ways to hide things from their wives, especially since he's one at home bringing in the mail! As much as you are gone through, he needs to be transparent with you. If he can't be, then you need to back off from this reconcialation a bit even if that means moving into the basement while he lives upstairs.
As far as the house goes, just don't. My poor husband tried just once to do the Lord of the Manor routine. We were working the same hours, though I didn't make quite as much as he. He got some idea that since I didn't make as much as he that I needed to do more of the household chores than he did even though I wasn't at home any more than he (we worked for the same company even!). I told him I would do exactly as much as he was willing, that a husband that loved his wife didn't play games like that. It took 3 weeks. He did nothing. I did nothing. Btw, it hurts a woman a lot more than a man to leave things undone. 3 looonnng weeks. No dishes, no dusting, trash didn't get picked up. Nothing. We went to work, came home, watched tv and went to bed. I didn't nag and if he complained I totally ignored him. I didn't repeat myself, argue or fuss. We had had these kinds of discussions before we were married and he had basically agreed that we'd share the chores, but his mama hadn't ever made him do much so he thought I'd be like her. Three weeks. I gritted my teeth everytime I walked to the kitchen.
Saturday morning after the third week, T says, I'll help if you want to clean up. And we cleaned up. I didn't brag, say I told you so or any of the above and I never had that particular problem again. This I might add all happened before the bad stuff. Even he laughs about it now. He knew he was wrong, but he wanted to know what I'd put up with. (sometimes men are children in disguise.

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Men have to suffer their own consequences. Your husbands consequence is that he has lost his authority. He'd like it back, but he needs to understand that with that authority comes great responsilbility that he can't shirk off on to you. And that is the responsibitility to care for his family: you, your children, his children from previous relationships and even alimony if he must pay it. It is certainly not your responsilbility to pay his child support/alimony, if you are doing so.
Umm, is paying for your tuition? Who is watching the kids while you are going to school and working? ARe you sure you are doing it all or is he contributing in ways you haven't counted because he doens't do things they way you want them?
He also needs to be very concerned that you aren't enjoying your career track. Disenchantment often means low job performance and then no job at all. It is a foolish husband who doesn't consider the wishes and needs of his wife. Right now, I'm not certain that he is your husband. With no more commitment than moving back into the house from him, I can't see that your marriage is any better off than when he lived elsewhere.
Sue is right. You have way to many problems to be dealt with on the BB. If he won't go to a Christian counselor with you, then you need to go by yourself. If you get any garbage about how you should submit to abuse, find a different counselor. As always there are good ones and bad ones. You need to find one that understands that your marriage is broken, not weak, not having a little trouble, but broke into little pieces that only the Lord can put back together. Let husband also continue where he is. I daresay he needs both. But you must take care of own spiritual needs in order to plan for the future.
Let me add that this isn't a reward situation. You are not rewarding your husband when you give back to him the responsibilities that he is supposed to be carrying already. God gave him his orders when he married you, it isn't a reward! Your submission to him is also NOT a reward. It is you following your orders that God gave you when you married. This is not a get what you can type situation. You are not breaking open a pinata to get the prize. Stop thinking of it as such.