anonymous, to find your grandma's sister its best to start with obvious records to ensure that you have the right person so the census (2 April, 1911) seems ideal for that (http://www.findmypast.co.uk/
(your grt-grandfather Fred reports that of total 6 children to date, two children have previously died)
SALKELD, Fred Head Married M 33 1878 Shunter Yorks South Bank
SALKELD, Ellen Maud Wife Married12 years F 30 1881 Yorks Middlesbro
CARLING, Jane Elizabeth Niece F 11 1900 School Yorks Middlesbro
SELKELD, Amy Daughter F 4 1907 Durham Shildon
SELKELD, Florence May Daughter F 7 1904 Durham Shildon
SELKELD, Mary Alice Daughter F 1 1910 Durham Shildon
SELKELD, Fred Son M 0 (6 MONTHS) 1911 Yorks
RG number: RG14 Piece: 29274 Reference: RG14PN29274 RG78PN1696 RD535 SD3 ED11 SN65
Registration District: Middlesbrough Sub District: Middlesbrough West Enumeration District: 11
Parish: Middlesbrough Address: 410 Cannon St Middlesbro County: Yorkshire (North riding)
Trying to find Mary Alice's birth in County Durham (1907-1911) with that name draws a blank so she must have been registered with a different name, or not born in Co. Durham. Amy's birth is apparent in Q1, 1907 Auckland (SALKELD Amy, Auckland, 10a, 228) so if Mary was born in Co Durham it would likely be in that Registration District (Bishop Auckland is near Shildon).
Assuming Mary's reported age in 1911 was correct (between 1 & 2) she must have been born between 3 April, 1909 and 2 April, 1910. There were only 5 girls born in this period in the county (http://www.freebmd.org.uk/cgi/search.pl
) Margaret Annie, Hilda, Maria, Phyllis and Ella so in order to exclude these births you would need to find them in the 1911 census in other families - the one that you can't exclude may be your grandma's sister. Searching for these young girls in the 1911 census shows us... Margaret is in Gateshead, Hilda is in Gateshead, Maria is in Lanchester, and Ella is in South Shields.
Only Phillis can't be accounted for but checking deaths, Phyllis died in Q3, 1910 (SALKELD Phyllis, 0, S.Shields, 10a, 429).
So as none of these births are your grandma's sister she must have been born outside of this period or in a different place, or both.
For more see comments below...