I do find Floyd and Pearl with their children (Bessie, Merrill, Gertrude and Cora) in 1920 Sullivan, Madison County, New York. At that time there is also a Webster Delamater living with them listed as father age 71.
The name in transcribed as Delammatter.
1910 also in Madsion County living with Webster
Name transcribed as Dlamatter
This could be yours, as they live in Sullivan, Madison County, New York which is where Pearl was living in 1910 & 1920
1900 Sullivan, Madison County, New York
Carter, Herbert E., head, 33, 8/1866, marr 4 yrs, Pa, NY, NY
Carter, A??, wife, 36, 6/1863, 1 child 1 living, NY, NY, NY
Mott, Pearl, step daughter, 17, 6/1882, NY, NY, NY
Carter, Tatha, mother, 76, 12/1823, NY, NY, NY
*Carter, A?? transcribed as Ana but could be Ava