I am perimenopausal on 2mg estradiol per day. one dr thinks my periods will eventually stop and one dr says they will not stop on estradiol. help?

Yes, will stop: In order to have a true period (menses), your uterus needs to build an adequate lining, you need to have exposure to progesterone, and then the progesterone drops low. Eventually you will stop ovulating and producing your own progesterone. If no one is giving you progesterone meds then yes you will stop having periods. Having said that, it's not healthy to be on unopposed estrogen too long.