My husband doesn't have a drivers license either, and i have cfs (chronical fatigue syndrome) and a license. In the beginning it gave some struggles between us too, cause he just sortof assumed that i'd drive anywhere, but i wasn't always able to because of my illness. He has come to realise, luckily, that him not having a license is his own fault and responsibility, not mine.
I've always made a point of it that he can go do things without me, that i'm physically not capable of. I don't want to hold him back. If he can't go somewhere because i won't drive, that is him holding himself back, not me holding him back. He now looks for alternative modes of transportation, or goes with someone else or so, if needed.
So on the driver part: make clear to your husband that you don't want to hold him back to go out with his kids, but that he'll have to do without you, because you are physically unable to. Also make it clear to him that driving when you're to tired (or ill) is simply dangerous. It is for everyone, and you are carrying baby now so you're risking an extra life/health.
He can look for public transportation, or go with like the grandparents or neighbours or friends. We spent 2 months in California without a car: we rented bikes and went by train and bus and such to go where we wanted.
On everything else: don't let him push you around. You need to take care of yourself ánd your baby. HIS baby. Don't push yourself to far, it'll hurt the baby too. Tell him when it is to much for you, and then take a rest. Let him deal with it.
I was going to say exactly what 19jellybean94 said. Tell him to get over it, it's time to put YOU first. As long as you are doing everything you possibly can to keep up with things, the extras can wait.
I'd be telling him to shove it up his a$$. He has 2 legs and a heartbeat, he can take the kids for a walk somewhere while at home doing your own thing... Your pregnant, have diabetes and on crutches. Why should you do everything for him and the step kids? Don't mean to sound horrible.