Cornelia Peacock was born on January 15, 1809 at Philadelphia to a Peacock Episcopalian family. In 1831, at the age of 22, Cornelia married the Episcopalian priest Pierce Connelly. The marriage produced five children.
In 1835, Cornelia and Pierce Connelly converted to Catholicism. In 1840, Pierce undertook the Catholic priestly vocation — requiring the Vatican-granted dispensation from Cornelia. Cornelia accepted the canonical separation and the vow of perpetual continence — producing the personal-institutional crisis.
In 1846, at the request of Bishop Nicholas Wiseman (future Cardinal Archbishop of Westminster), Cornelia founded the Society of the Holy Child Jesus at Derby in England — the American-English Catholic congregation dedicated to the Catholic education of girls.
In 1849, Pierce Connelly apostatized from Catholicism and undertook the systematic public campaign to restore his marital rights over Cornelia — producing the famous Connelly v. Connelly English court case (1849–1858) in which Pierce attempted to force Cornelia to return to him. The English courts initially ruled in Pierce's favor, but the Judicial Committee of the Privy Council reversed in 1858, institutionally recognizing Cornelia's religious vocation.
Cornelia served as Superior of the Society until her death at Mayfield on April 18, 1879.