I too have been working on my familty tree on my mother's side. John Dwyer/Mary Redmond would be my GG Grandparents. My G Grandmother was Mary Catherine Dwyer married to Thomas Whittingham (Liverpool). I have found John Dwyer/Mary Redmond's Marriage information. John Dwyer, born 1841 (Ireland). Mary Redmond, born 1844 (Ireland). Married 07 Feb 1864, St Marys-Sandymount, Dublin, Ireland. It lists Edward Dwyer as John's Father and James Redmond as Mary's Father. Also, the record shows Witnesses for the wedding as Andrew Redmond and Catherine MCCabe. Catherine McCabe is also a Redmond. I found her Marriage to a James McCabe and James Redmond is listed as her father with John Dwyer listed as a witness. They were married on 17 December 1863 at St Mary, Haddington Road, Dublin.
It would be appreciated if you would happen to have any other information to add, especially from Ireland. My Mom and I have records and information once John Dwyer/Mary Redmond arrived in Liverpool and then forward. Mom will be 83 this year and has some good memories and knowledge of her family.