BB1, that's a difficult life! Does your husband seem like he wants a divorce? Perhaps there needs to be an effort to connect with your husband on a husband-wife level. To find a way to spend some time with him one-on-one where the atmosphere is conducive to talking and listening to his side of the story. Perhaps he doesn't see how his actions affect you or doesn't realize how selfish he is. Or maybe he doesn't know how to respond to you so he lies or stays away. It seems to me that he should be smart enough to see that you need help, and should just offer to do it, but the way he's acting sounds similar to a lot of men. After all, who really wants to do all that unglamorous stuff? As long as you're there to do it, and he's not forced to do it, there may not be enough incentive for him to pitch in.
As to whether to divorce, what do you want in the long term? In ten years your kids will be able to take care of themselves more, your master's degree will be done, and life will hopefully get easier. Do you want to be with your husband then?
Also, how will divorce affect your kids' wellbeing and the family's finances? How you feel about your husband is critical and important, but they are also a big factor in the decision. I'm sure you want to do what's best for them.
I guess I'd ask why you jump straight to divorce as the most likely solution? You could always separate and work on improving yourselves. Or you could try really hard to re-connect and communicate with your husband and see if he's responsive.
There are people here like myself who'd do anything to avoid divorce. It's hard to see divorce as something that would solve your problems, but if you feel you tried everything there might be people who would encourage you to do it. On the other hand, it's great that you and your husband re-married. There must be something that brought you back together. I hope you can re-discover it!