Your question is interesting, but I will have to look up some things before I can give you any kind of real answer. I have a copy of John R. Bozarth's will, and, if memory serves, that is where I found the married names of the girls. Of course, that was 1907, so Annie E. had already passed. I have a notation that Annie's last name was Kerns, but no indication of her husband's first name, and no idea off-hand where I got that information. I was really bad at noting sources when I began all this.
It seems unlikely that both Annie and Harriet would be called "Hattie" - but Harriet would only have been 13 in 1884 [she was 9 in the 1880 census], so it's unlikely that your "Hattie" is Harriet. That's the real puzzle, isn't it?
I will look through my notes on the Bozarths and see if I can clear this up. I was primarily interested in the family's connection with my great-great grandmother, who appears with the Bozarth family in the 1880 census as "M.P. Adair." After an extensive search, I now know that the "Aunt Molly" who raised my gr-grandmother Piaetta [called Etta or Ettie] was Mary Bozarth, wife of John R. Mary's maiden name was Williams; Mary's sister Martha is Piaetta's mother. Harriet Oskins was their mother, and the reason I could never find a Bozarth-Oskins marriage was because Harriet was married three times, with children from each marriage. Mary and Martha were the children of her second marriage, so not Oskins at all.
In short, I am not related to the Bozarths, so I stopped looking in that direction once I got the answers I was looking for about "Aunt Molly." I did, however, inherit some photos that are Bozarths and may even have a snapshot of the elder Bozarths, but I can't be sure as it has no caption. My grandmother, or perhaps her mother, evidently kept in touch with the family for many years.
Give me a few days to hunt this information up, and I will see if I can answer your question. I hope I can.