Our Elizabeth Cole was born in Chichester, West Sussex and married James Clarke. They had three children, Caroline, Mary Dash and James Cole (Cole now becoming a middle name). She died in June 1886 in Widley (now known as Cosham, Hampshire), UK.
I think the names and dates are just a coincidence, though based on past experience I bet you get more responses here about your family than we do about ours. Good luck!