There is this "Kate L. Mattison" (or Matteson?), a boarder in NY in 1900 - she is listed as a teacher, b. Sep 1875. Details say "b. NY parents b. NY", but possibly worth further examination? There seem to be some other teachers on the same page as the census - perhaps they worked together.
https://familysearch.org/pal:/MM9.3.1/TH-267-11899-167221-13?cc=1325221
She still would have been quite young when her father died, do you think she would have lived with one of her uncles or were there members of her mother's family around?
I'll keep that one in mind and everything is worth more investigation.
All the members who came to U.S. lived together as in the 1880 U.S. census as attached in my original post a few pages ago. Indeed I have not been able to trace them in any censuses after this date.
Daniel Matheson(father) died in Manhattan (in gruesome circumstances!) in November 1886.
Ellen Matheson(mother) died in Washington D.C. in December 1879.
Roderick Matheson(uncle) died in Manhattan in January 1890.
Helen Matheson(aunt) died in N.Y. in 1896.
I have not been able to find anything of the three children after this date.
Frederick John (born Manchester, England in September 1866).
Ellen (born Edinburgh, Scotland in May 1868).
Katherine (born Washington D.C.(assumed), in 1874, and according to family anecdotal evidence, a teacher in New York and living at some time in Gramercy, N.Y..
I did find the father mentioned in D.C and N.Y. City Directories up until his death, but of course only his name appears as he was the head of the household. I searched for the children in the Directories after the adults died but without success.