I've just ordered the 1863 Amy Isadore Sutcliffe birth certificate. Fingers crossed it'll help either rule in, or conclusively rule out this Amy as the other Amy's daughter.
The birth certificate has arrived! This is what we've got;
14th May 1863
11 Trafford Terrace, Moss Lane, Hulme
Amy Isadore - Girl
Father: John Sutcliffe - Mariner
Mother: Amy Sutcliffe formerly Rothwell
Informant: John Sutcliffe, Father, 11 Trafford Terrace, Moss Lane, Hulme.
Registered: 10th June 1863