I just want to say that I admire any mom who goes back to school, especially when the program is an overtime commitment like nursing. Y'all are my heroes!
Mommy2010, you will be OK if you just get started and roll on through! Your kids are pretty young, but you can start small and do one or two pre-requisites at a time; they are usually scheduled to be convenient, only a couple times per week in the daytime or evening. Once you get into the swing of studying and taking care of the family all at once, the transition into nursing school will still be tough, but doable. The more you do, the more you can do.
As for the kids getting sick, just make sure you've got a good support system in place. Piece together a list of people who can probably help you out from time to time:
-Your husband, especially if he works days and you get accepted into an evening/weekend program (hopefully y'all could arrange a date night every now and then =/)
-Moms, sisters, friends
-Any college-age baby-sitters looking for work a couple afternoons per week (as someone who did this all the way through my first college degree, it was my favorite job - cute kids, great families, and a little money to sweeten the deal. If you can find two or three girls who would alternate days watching the little dudes, that might be a good way to make sure they have someone without spending too much money)
Whatever you decide, best of luck!