Do colleges check to make sure you REALLY listed all of your previous education on admissions application?

Ok...I am definately not usually one to mislead! When I graduated from HS I went to community college. I became a single parent later that year and was unable to do as well as I had hoped. That in combination with a serious math anxiety added up to me F'ing up kinda bad. Now I know what I want to be and that is a nurse....it is my ultimate goal and I want to know if I do not list community college and only my trade school info will the college I am applying to be able to check on me somehow and catch me? Please help!

No...colleges will NOT do background checks on you. Though you should know that not listing your experience at other colleges is a violation of the application process and if it were to come out and they wanted to be sticklers...you could be kicked out of the university.
To be honest though, I'd put it on there, it generally won't hurt you as a simple meeting with an admissions counselor will ease your fears over such things. The bad grades are even less fearful because most schools have what is known as academic renewal, which means grades earned more than 5 years ago don't generally count against you. So it sounds like you'd be in this boat.
It's always best to be honest with your college, they deal with this sort of thing all the time.

probably, if you sent your transcript to the community college it could be in the records that it was sent there.

A few bad grades (which you'll get a chance to explain either in an interview or in a supplemental page on your application--send one!) won't hurt you too much.

Lying on your application (not just a mistake, but actual lying) will ruin your academic career for the rest of your life.