Was there a Catholic couple who separated but did not divorce so that one spouse could enter religious life?

You may be thinking of Cornelia Connelly (1809-1879), who with her husband Pierce, an Episcopalian minister, converted to the Catholic Church. Pierce decided he wanted to become a Catholic priest, but, in those days, no special dispensation existed to allow an Episcopal priest convert to be ordained and share a common life with his wife. To accommodate his vocation, Cornelia became a nun and founded the Society of the Holy Child Jesus.
Pierce’s vocation did not last. He eventually left the priesthood and the Church altogether, denied Cornelia contact with their three children, and pressured her to abandon religious life to resume life with him and the children. She refused and entrusted her children’s future to God. She has not yet been canonized, but she has been declared venerable. You can read more about her in Ronda De Sola Chervin’s book The Kiss from the Cross.