Transcript worry and questions

Over the last few years, I quite frankly bombed out of college. After taking some time off to deal with personal issues and such, I decided to return to college. I applied as a part-time student to a university and in the process did not tell them about my previous college experience. This university’s policy is that a student cannot take courses there if their GPA at a previous institution was below a 2.0. I have decided to rectify this failing by taking enough courses at my old college to raise my GPA there to a 2.0, which I could do within a semester. I personally feel that I made a large mistake by hiding my transcripts.

My questions is, is there a way for me to update my transcript at the university I am taking part-time courses at without possible blacklisting myself from that university or losing credit from the courses I have taken? Also, if I intend to apply to said university as a full-time student, I assume including my old transcript, even if improved to a 2.0, would reflect negatively. I am currently doing quite well as a part-time student and would like to know the best way to plead my case when I send in my previously hidden transcript. Thank you for any advice.