About your questions: Do you think Esther/Hester remarried after her husband died? I do not know, but would like to find out. I do not believe so based upon family records, however.
Do you think Esther/Hester may have died in Connecticut?
In 1880, she can be found on the Census for Monroe, Michigan, NA Film #T9-0596, living with sonJames Olmstead. I assume she died there, but would like confirmation.
I believe that Esther's/Hester's siblings went to New York State, do you know anything of this?
If you read my other posting, then we have a mixup of Hester's. I don't know about the other Esther.
Children of Hester Janet Mix & Richard Montgomery Olmsted/Olmstead:
James Monroe b. June 06, 1824 died Sept. 6, same year Rutland, VT prob.
Hannah Louis married Nicholas Barlow of Detroit MI.
Louis Montgomery b. April 28, 1828 Rutland, VT - d. April 06, 1857 unknown location.
William Mix Olmsted b. November 24, 1830 Rutland VT. m. Caroline Roney, unknown location -- unknown death dates.
James Munroe Olmstead b. January 27, 1833 CT prob. married Eliza Tiffany and lived in Detroit & in Monroe, Monroe Co., Michigan.
Martha Julia Olmsted b. February 24, 1837 either New Haven, CT or Rutland VT. She was a twin and married a Loomis. Family records state she was a widow in Chicago, IL and I do not know what happened to her. Her daughter Georgiana married a Sprague. Would like to know the first names of their spouses, marriage dates, etc.
Mary Jane(Martha's twin) born. Feb. 24, 1837 was a tutor, suffragette and author. Mary m. 1st June 22, 1856 Charles Starr King in NY City -- 3 children, Jessie Ida King b. May 12, 1857 never married, May Starr King b. September 12, 1860 m. Henry B. Pasmore, an opera composer & Charles King b. December 19, 1863 never married. The entire Pasmore family was very musically talented.
Mary married 2nd Jesse Turner Hanks April 15, 1869 in New York City. He was a manager of a gold mine in California and died in 1872 in Downieville, CA. One child: Edmond Hanks who was put in a children's home and adopted at the age of 4 by a family in Indianapolis who renamed him Edgar Hanks Evans. He never saw his mother again, but met his siblings as an adult.
Mary married 3rd Andrew Palmer Stanton May 10, 1875 (no children.) He was a newspaper publisher (The Argonaut)of San Francisco, CA. Mary died , died March 05, 1914 in Union City California prob. in a nursing home.