Staffordshire do have a useful website

Staffordshire Birth Marriages and Deaths

http://www.staffordshirebmd.org.uk

This is REDMAN - mother's maiden name JENKINS from the website (all the births certificates would confirm, if mother is Sarah)

REDMAN - Doris - Longton - 1902
REDMAN - Arthur Sydney - Longton - 1901 (A/M/June Qtr 1901) possible death 1901 S-O-T Arthur Sidney REDMAN ***
REDMAN - William Henry - Longton - 1899 (Possible death - July Qtr 1901 - Stoke on Trent)
REDMAN - Sarah Hannah - Longton - 1897
REDMAN - Evan Neary - Longton - 1896
REDMAN - Evan - Trentham - 1894
REDMAN - John William - Trentham - 1894
REDMAN - Alice - Trentham - 1892

(in bold the 3 children you mention) need to see if the other children are around in 1901/1911??

and the marriage is also on the above website

Sarah Hannah JENKINS married William REDMAN - Civil Marriages (Stoke 1891)

1911 Census - 64 Wade Street, Burslem

William REDMAN - 39 - Carpenter, born Longton
Evan Neary REDMAN - 15
Doris REDMAN - 8
Edith McLone - 39 - Widow, Housekeeper - born Brocton, Staffs
William REDMAN McLone - 5

Looking at the StaffordshireBDM -

William Redman McLone - mother's maiden name BUTTERY - 1905, Longton, Stoke on Trent

and from the Staffs Website

Frederick McLone married Edith BUTTERY Civil Marriage Stafford 1888

1901 Census Longton
27 Trentham Road

REDMAN

William E - 63
Sarah - 57
William - 29
Alice - 7

If Arthur Sydney REDMAN is the child of Sarah Hannah nee JENKINS - this could tell you where he was born etc.

As Doris was born in Stoke workhouse - Do you know from the 1901 census the residents of the workhouse

Staffordshire Name Index (hold Workhouse records - search for Redman without any luck)

http://www.staffsnameindexes.org.uk/StartPage.aspx?