A possibility?

Arrived New York 13 May 1885 aboard the ship "England"

C Butcher Female 50 (described as "wife" but no husband travelling)
Henry Butcher 19 Labourer
Emily Butcher 11 Child

Last residence looks like Yorkshire, but as a Henry Butcher b 1866 Pebmarsh is in the 1891 census boarding with a family in Walthamstow, I'm not convinced its the right family, but still....

A Cathrine Butcher aged 73 is on the 1900 US Census at Bennington, Marshall, Illinois with son Henry aged 32, and there is a Find a Grave image showing her dob as 17 Jun 1827, died Mar. 12, 1907.

Emily possibly married a Thomas Vincent.

Hope Im not sending you off on a wild goose chase....