Is my wife required to enter into a state of ihram for Umrah from the miqat after she has purified herself, or should she enter into ihram from Jeddah, where she resides, knowing that she intended to perform Umrah from the Eastern Province and began her menstrual period during her flight to Jeddah?

Menstruation does not prevent the validity of assuming ihram for 'Umrah. Your wife was obligated to assume ihram for 'Umrah from the miqat she passed. If she did not do so, she has erred and is required to return to the miqat and assume ihram from there. If she does not do so, a dam (sacrificial offering) becomes obligatory upon her. Jeddah is not a miqat except for those who initiate 'Umrah from it.