I think the child you are referring to is the one I have listed as Adelia Fulton (called Dell in 1880 census, went by Delia), daughter of Robert Nero Fulton & Cordelia Taylor. She was born March 11, 1877 in Fletcher. She was working as a waitress in S. Merrimack, NH when she married Marion Smith at Nashua, NH on Christmas 1897. She died of consuption (TB) on March 30, 1901 at Goshen, NH. I know she had three children: Robert Marion, 10/1898, Minnie Myrtle, 12/6/1899 & William Craig, 5 days before her death.
I don't have much on her. I know that her parents had moved from Fletcher, VT to Goshen NH by 1900. Her sister Rachel had died in Fletcher in 1885. All other siblings either married before that period in Vermont, or after 1900 in NH so can't narrow their move time any more than between 1885 & 1897.