Who were Jane's parents?

Jane Francis O'Conner and Robert Willis were married in the Roman Catholic parish of Roscommon and Kilteevan on the 6th of April 1834. Who were Jane's parents?

Theirs is a romantic story. Robert was a 26 yr old Protestant constable from Fermanagh who got Jane in the family way. They ran off together, were found by the local parish priest, brought back and married. Witnesses to their marriage were Edward O'Conner and Margaret Willis. Jane and Robert were separated after their wedding, their first child, Edward born four months later. Jane was not allowed to live with Robert for three or four years, "until she came of age". This also perhaps because Constabulary regulations stipulated that a constable must serve seven years before he married. Their second child Robert was born in 1838. Their's was a successful marriage and Robert enjoyed his Constabulary life, choosing to stay in Ireland rather than joining his brothers (unknown) in America or children (known) in New Zealand.

Was Edward O'Conner related to Jane Francis O'Conner? Was Margaret Willis related to Robert Willis? It is tempting to think that they were parents, negotiating a respectable outcome with Church and Constabulary for this wayward young couple. I'd love to know the truth of it!