On Nora Eileen's birth certificate, who was the informant?
What was the address of birth, and the address of informant? (May be the same when the informant is the mother).
Dorothy Mottram who was sailing to Canada in 1920 is not the same girl as the Doris you found - entry form into Canada shows she was born Toronto:
http://www.rootschat.com/links/01hjw/ Mrs A Mottram was born Cheshire, and had been in Canada since 1910 (find this entry by going to page 4518 on above link)
Something that might be of interest - Agnes Clee m. Edgar Hutton in 1930 in Middlesborough, also Agnes Hutton d. 1940 there aged 50.
Also Ivy Mottram married in Middlesborough 1928 to John T Owens (two children on indexes, Ivy possibly died in Yorkshire, 1964 aged 58)
Agnes and her daughter Ivy?
There are other possible Ivy Mottram births of a similar age but the others seem to line up with marriages in their areas of birth:
Ivy b. Nottingham 1905 - probably the 1925 Nottingham marriage
Ivy b. Macclesfield 1906 - probably the 1925 Macclesfield marriage
Ivy b. Nantwich 1908 - probably the 1932 Nantwich marraige