Why do your parents want you to attend UMBC? Is it an issue of cost? Can they afford to send you to Rutgers, and is Rutgers offering any aid?
Yes, if you attend another college and want to transfer, you will need to apply as a transfer and be accepted as a transfer. The GPA that you will need and other requirements for for transfer applicants should be available on Rutger’s website. However, in another two years, these may be different, so you should look again when you are thinking to apply for a transfer.