I wouldn't say that you're dreaming big, many nursing students are non-traditional nowadays. At my college, I see people fresh out of high school along with 60 year old's who want a change. Taking a few years off is not going to put you at any sort of disadvantage. The best thing about college is that it ISN'T high school. Your past circumstances won't dictate how you do in college, only your passion and dedication will.
As far as not being accepted, just keep your goals in focus and do as well as you can in all the pre-nursing classes. Start studying for nursing school entrance exams, and if possible, apply to as many colleges as you can. Really the best thing I can say is don't have a preconceived notion about who you are and what you're capable of because of teenage years. I'd say if you're truly dedicated and know what you want, you have a great chance of being accepted. Good luck!