If you quit school, you'll not only be shortchanging yourself & your kids, you will always resent him. If you keep going to school but don't do anything for him, he'll keep resenting you. So it seems like you've got to do something.
I feel like there are two ways to try to deal with this:
You could get him talking. You must keeping silent - no defending, explaining, or justifying. Just ask questions and listen. Think hard about what he says. What is he objecting to specifically? Is it the time away? The money? The irregular schedule? Feeling of alienation that you're doing something he doesn't understand? Feeling threatened by realizing you'll be making a great income and perhaps soon won't need him for financial support? Try to tease out why specifically he's having issues with. If it's something reasonable & changeable, do your best to change it (eg. the number of hours you spend with him & the kids).
The other option is to commit to meeting with a couples counselor. This may be helpful, no matter what. Sometimes the relationship problem may be due to a individual's problem (eg. depression), and a good counselor will pull that person aside and help them with their own individual issues. If he's having insecurity issues, it might be better for your relationship, if he can work those out with the counselor. You can show him you care, but you can't be his shrink or his security-blanket.
My heart goes out to you, because it is hard to be in nursing school
and it's so much harder with kids to worry about and an unsupportive spouse. This is such a nice forum because so many of us have struggled with school vs relationship conflicts. I feel your pain!
Even if I can't fix your relationship, I am here if you need to vent to someone who understands.