Shazzie
This is odd!
You are looking for a child named Mildred, born to someone named Julia Ann, who, at some time, married Thomas Nevins.
We have got a definite marriage in April/May/June 1906 between Julia A. Hill and Thomas Nevins, followed in November 1906 by the birth of Mildred Hill Nevins.
There is no other marriage of a Thomas Nevins to a Julia on the County Durham site (which has complete coverage). Does your mother have any idea where Julia married Thomas?
The marriage and birth are outside the time-frame you have given, but the coincidence of names is amazing!
Is your mother positive of all the information she's given?
Jennifer