I also felt that the young lady in the OP picture appeared to be in her early 20s at most. Although Margaret "Molly" Brown was married and had a family by that age, her husband J J Brown did not strike it rich till 1993, by which time 'Molly' was 26 years old.
Yes , the clothes on the OP woman appear too expensive to have belonged to Molly Brown during her "common" days. That hat alone would have been out of her range, even as part of a Sunday Best outfit.
Then there is the
chin, of course.........
I looked up some old pictures of Jeanette Jerome and while in some of them she appears to have a slight cleft chin, it was in no way as pronounced as the one belonging to the young lady in the OP. Also, while the OP picture could have been digitally enhanced in contemporary times, that kind of sepia toning did not become popular till the late 1880s, by wich time Churchill's mother was in her mid 30s.
View attachment 116765
Above is an authenticated photograph of Jeanette Jerome taken by Jose Maria Mora around 1885, when the lady was 31 years old. As we can see, the features are quite different from the one in the OP.