If you haven't taken any prerequisites, we can't really tell you about your "chances". That said, do not take your DAT until you have confidently passed the prerequisite classes covered by the exam.
There have been dental hygienists who have gotten into dental school so you can do it. The personal challenges however are yours to address that an anonymous forum won't be in a position to give advice. But if you think it is worth taking the chance, I hope you can go with a lot of support.