Are you working a true EVENING shift or a GRAVEYARD shift? I don't think you are helping yourself or your children if you need to sleep 1/2 the day and I don't think you would help yourself or your children if you don't sleep more then 2-4 hours per day when you can get them to nap or hubby or someone lets you sleep for a bit.
If you work an EVENING shift you likely need someone to care for the children at least part of the day when your husband would have not come home yet. So I'm going to take a stab in the dark and say you are working the overnight shift and that's why you hate it. If you do the 3 day, 12 hour shift thing then I know many moms just do without sleep and exhist on 2 hour naps. Again, it's horrible.
I care for children from time to time with moms that work these shifts. It NEVER lasts very long. They change jobs often because of how hard it is.
Missing a little time here or there for a child's illness is just part of the mom territory. I honestly believe from what I've seen in 24 years of providing care and seeing how these shifts wear down moms and families, not to mention no time for the marriage, full-time daycare is better than mom trying to be super mom and keeping them out of daycare at the expense of so many things that will fall through the cracks.
If you make enough money to pay around 375-450 per week, you could likely find a middle aged mom, newly empty nested and previous stay at home mom type to nanny for you. In that case, you wouldn't have to worry about missing work to sickness. But I honestly believe the kids are better off with mom when they don't feel good.
I did want to clarify that one of my moms keeps very strange hours, is in nursing school and often does overnights. But she pays for full-time daycare during the day so she can sleep or study or work, whatever is needed. She makes time for herself, as little as it is, and keeps her sanity. The point I'm making is that no matter what shift you are on, you need help if you want to have your sanity, keep your marriage alive, and not short change your children by being tired and stressed out all the time.