Dear Rev. Fr. Elias:
Actually it is my understanding that the sisters are third order, only the enclosed 'Poor Clares' themselves are second order. Mother Angelica's community are a third order group (not of poor clares, per se), but of 'poor clare's of perpetual adoration'. Their enclosure is part of their foundation, but it is not the papal enclosure of the poor clares (2nd order). They were founded from Canton, Ohio. They are not strictly cloistered (solemn papal enclosure) like the poor clares, or the carmelites. I have been to their house in Canton, and also their small monastery in Washington D.C. (near Catholic University).
The 34 nuns of Our Lady of the Angels Monastery in Hanceville, Alabama are Poor Clare Nuns of Perpetual Adoration (PCPA).
They are a Pontifical contemplative order of cloistered nuns and are afforded the privilege of solemn vows, Papal enclosure, and solemn exposition of the Most Blessed Sacrament.
Yes, Mother Angelica's community originated from the Franciscan's community in Canton, OH, where Mother Angelica, as Sr. Rita, took her permanent vows.
Mother Angelica's congregation has only 5 Extern Sisters who live and work outside of the cloister. These Sisters take care of the OLAM Shrine, the "public side" of the cloistered community, and other "mundane" activities.
The Poor Clares are part of the Second Order of Saint Francis of Assisi.
(BTW, the Monastery's address is at Hanceville, AL while that of EWTN is at Irondale.)
AmdG