Hello C.,
First of all, I'm a guy. Second, I have a son, Third, I am married to the mother of my child. Last,I married her before we had our son, way before. Thats where I'm coming from.
Not like any of this is news but sometimes its good to hear this stuff from someone who has no investment in your situation, so... here goes.
Women do have more to worry about than men do, because if the guy takes off, everything is on her. And most women don't ever think that leaving their children is an option, so they HAVE to be responsible so that their kids get to eat and live indoors.
Most guys like to THINK that they run their own lives, and especially if they come from a particularly patriarchal culture, they can get pretty goofy about what is womens work, and what their response should be to womens' demands of their time and attention. Anything that threatens their sense of 'the male role' is usually met with defiance.
Don't get me wrong, there are a lot of good guys who do good stuff for their families, but those same guys often have a really hard time coming to grips with the realities of todays economy, and the inherent unfairness of the treatment of women in the culture they were raised in.
The jealousy thing in a big warning sign that he is feeling insecure and threatened by your actions, and most Macho guys who get jealous are more worried about what their family and friends(who were raised in the same culture) think about them, than what you need. This is a problem. YOU should go see a counselor, by yourself, (he won't understand your need to bring 'your problems' outside the family, so do it yourself and discreetly) and find out what tools they can give you to deal with HIS problem.
Hopefully you can learn some ways to talk to him that doesn't make hime defensive and gets him to open up and share his worries with you, instead of triggering his anger and jealously.
Also, many guys just never grow up. The irresponsibility of not having a license, and letting you do all the child related tasks does not show much concern for you or your welfare. If he was mature enough to think for 2 minutes about everyone in the house besides himself, he would be able to see that by refusing to help in the way that YOU NEED, and this includes him taking care of his medical issues, he is basically saying that he does not care about what you want, why you want it, or what it means to you.
If he wasn't trapped in a way of thinking about women that makes your needs a threat to his status as a man, he would see that the best way he could show you that he cares for you, is to do whatever it takes to give you every kind of security you need that he is CAPABLE of providing.
I'm sure he is a good person, you just need to help him grow a bit (as if you don't have enough to do). If he's man enough to meet the challenge, you'll get a better partner, one who realizes that in order to rule his kingdom, he needs to be what his people NEED him to be. If he's not willing to evolve, don't waste any more time, find someone who is.
I wish you well.