First, it sounds like he's addicted to video games. Yes, this is a real addiction. I actually have a friend who divorced her husband over it (he met another woman in his online video game. Never any physical hanky-panky, but emotionally, he cheated. He, too, would stay up to all hours of the night playing, wouldn't help with housework or childraising.). Your husband needs help in learning how to turn off the games. He might find that he has to give gaming up altogether.
Second, it sounds like your husband is depressed. Try having him take some vit D3 (you can buy caplets that have 2,000 mg) now that it is winter time and see if that helps his mood. Tell him the Vit D will help keep him from getting sick/will strengthen his immune system (because it does). I know you live down South, where there's more sun, but if it's cloudier in the winter time, or if he's inside all the time and never in the sun, it is likely he is Vit D deprived.
Third, helping with the kids--did he want kids? Marriage is about two people working together to make it work; being parents is about two people working together to raise the children. My husband works full time out of the house; I'm a stay at home mother WHO ALSO works at home as an editor (I used to work full time out of the house until our daughter entered school). My husband knows that I am not at home doing housework and/or childcare duties all day while he's at work; I am ALSO working. Therefore, he has to help raise the child and do some housework as well. We don't have a superclean house, but it's picked up and liveable. I refuse to put all of my time and attention into the house when he lives here too; it's up to both of us to do the daily household grind/chores. Just like it's up to both of us to parent our child.
Perhaps your doing everything while you worked full time outside the house set your husband up with the expectation that you're Super Woman and, now that you stay at home and don't bring in any money, your husband still expects you to be Super Woman. Especially since you're not bringing in any money.
Your husband sounds like he needs a mommy. My husband thought he'd pull that one on me when we were first married. I told him if he wanted a mommy to take care of him, there was the door. He was welcome to go back home and live with his mommy. I wasn't his mommy. We had our daughter two years after we were married. He tried pulling the "you're my mommy, take care of me" routine again. I told him there's the door; you can go home and have your own mommy take care of you. He's never tried it again. He knows I'm serious. I would boot his a$$ out so fast, his head would spin. He loves me, loves our daughter, and would seriously never do anything to lose us.
If your husband has the expectation that you will take care of him, the house, and the children--and you've been doing everything since you were married--he sees no reason to change anything. Why should he? He's got it made--he's got you to do everything for him.
You will have to decide if he can be changed, if he wants to change, and how much you want to remain/keep taking care of him. I have known a lot of women who have divorced their men simply because the men took advantage of them/treated them like they were their mommy.
I want a partner in my marriage; I don't want to play mommy. It took a while before I got my husband to understand the fact that I wasn't going to be his mommy. If he needed his mommy that badly, then he could leave and go live with her. Every once in a while, I still have to remind him that I'm not his mommy. BUT, I nipped that issue/problem in the bud right when it first started. I'm afraid I don't have any answers for something that's been going on/perpetuating for a while. Counseling is the best option, I think, for you, even if you're the only one going. It will help you see things in a clearer light and decide what it is you want to do. The counselor might even have some ideas as to what/how you can phrase things you say to your husband and how you can go about getting him to help/cooperate.
Just remember: he's been counting on you to do everything so he can remain a little boy/doesn't have to grow up. It's not going to be easy to get him to change; he might completely refuse. Then you'll have a choice to make. Do you stay with him, knowing you'll have to do everything, or do you leave him. Since you already do/take care of everything, living on your own with your children shouldn't be that hard. It will/might be an economic struggle, depending on what your degrees/work experience is.
You have to decide what you want, how happy you want to be. Don't let him drag you down, just because he hasn't decided to grow up and do his part in the marriage/household/childraising arena.
And for those who say working full time and bringing home the paycheck is stressful--so is taking care of the house and the children full time. That is also a job, a job that is far, far more stressful than working in an office. I've done both; I much rather prefer working at home, but the chores still need to get done. And it's not fair that I am the only one who is expected to clean house when another adult lives here as well. A marriage is a joint adventure; that means, two people have equal responsibility. For everything.
And a little tip: as a mother, you need to take care of yourself/pamper yourself, too. If you aren't able to sleep in, try taking a short nap in the afternoons. I say this as a caution to all mothers out there, whether working full time out of the home or working as a stay at home mother: you need to take care of yourself. Especially making sure you get enough sleep. It is SO EASY to deplete your adrenals and then end up with lots and lots and lots of health problems. I know; I'm one of those whose adrenals are depleted (I have moderate adrenal fatigue). I've been working for 4 YEARS now to get my adrenals back to full function. If you're tired; rest. If your husband says something about it, tell him a little nap now vs total collapse/chronic fatigue or fibromyalgia later, take your pick. If you end up with one of those chronic illnesses, you WILL NOT be taking care of the children, the household, or him. Trust me; you don't want to wait until your reserves are depleted. Take care of yourself now, in any way you need to. And that includes good-quality supplements to help make sure your body has what it needs to function optimally. First and foremost, as a mom, you want your body to be strong so that you're healthy and can be there for them.