We have a woman who is Catholic but has been away from the Church for many years. She has been studying with the RCIA each week. Can she be part of the Rite of Election?

NO. The Rite of Election is reserved for those who are being fully initiated at the coming Easter Vigil. By exception those who have been baptized in another Christian tradition but are uncatechized and are coming into full communion with the Catholic Church may be part of the RCIA process. They are recognized at the Rite of Calling Candidates to Continuing Conversion when combined rites are celebrated.