This is the death certificate of her daughter. It gives her maiden name as Martha Rodgers.
↑ Name at the time of her marriage to John Byland. (Whether this was a previous married name or the name of a step-father has not been determined.)
Alternately, Harkins might have been her maiden name and Rodgers might have been the name of a step-father or a married name after John Byland died - sometimes informants are confused and give a subsequent married name instead of a maiden name. However, taking the death certificates at face value, her maiden name was likely Rodgers.