I've been off on medical appointments and been checking the information. Here's what you have kindly found for me, plus my own research.
Re: Children of Sarah Welch
William Edward Withers. Baptism Register: Baptism Register: St Martin in the Bull Ring, Brmingham P700; Birmingham Archives & Heritage, 1839-1844, DRO 34/18 (FindMyPast). Marriage Registration: Aston, Warwickshire, 1867 TBV Vol 6d p321; Anne Elizabeth Whitfield William Edward Withers (Ancestry.com). Death Registration: West Bromwich, Staffordshire, 2nd Qtr 1839, Vol 6b P764 (Ancestry.com).
Clara Harriet Withers. Birth Registraion: Aston Union, 1st Qtr 1841, Vol 16 Page 173 (GRO). Baptism Register: St Martin, Birmingham, Warwickshire, 4 May 1843 (FindMyPast). Marriage Registration: West Bromwich, 3 Qtr 1865, Vol 6B P797 (FindMyPast). Death Registration for Clara Shorten not found.
Amelia Withers. Birth Registration: Aston, Warwickshire, 2nd Qtr 1843, Page 180, Vol 16 Line 4, (Ancestry). Baptism Register; St Martin, Birmingham 4 May 1943 (Ancestry). Marriage Registration: West Bromwich, March 1868 Vol 6b P697 (FindMyPast). Birmingham Daily Post, Wednesday 15 March 1882, p8; (British Newspaper Archive). Death Registration: Birmingham South, Warwickshire, 3rd Qtr 1928 Vol 6D P7 (Ancestry).
Samuel Francis Withers. Birth Registration: West Bromwich, 1st Qtr 1845, Vol 16 Page 321 (Ancestry). Marriage Registration: King’s Norton, 4th Qtr 1873 Vol 6c Page 881 (Ancestry). Death Registration: Bromsgrove, 1st Qtr 1910 Vol 6c p227 (Ancestry).
Sarah Elizabeth Withers. Birth Registration: Birmingham, 4th Qtr 1846 Vol 16 P303 (FindMyPast) Marriage Registration: West Bromwich, Staffordshire, 1st Qtr 1868 Vol 6b p697 (Ancestry). Kelly’s Directory of Birmingham 1872 ‘Builder’ (Ancestry). Aris’s Birmingham Gazette, 11 January 1868 (FindMyPast). 1881 Census, RG11, Piece 3017, Folio 11, Page 13, (Ancestry).
Edwin Frederick Withers. Birth Registration: Aston Union, 3rd Qtr 1848 Vol 16 p182 (GRO). Death Registration: Aston, Page 124 Volume 16 Line 161, 4th Qtr 1848 (Family Search). Burial; Key Hill cemetery, 1848 WITHERS Edwin Frederick, 6402 Graves E 58.
Fanny Louisa Withers. Birth Registration: 4th Qtr 1849, Aston Union, Vol 16 P170 Line 80 (FamilySearch). Marriage Registration: Hanover Square, 4th Qtr 1880 Vol 1a p754 Line 119 (Family Search). 1891 & 1911 Census RG14 Middlesex, Kingston 40, Enumeration 14, Piece 3574 Schedule 236 (Ancestry) 4 Walpole Place Teddington. Death Registration: Paddington, 2nd Qtr 1944 Vol 1a p353 (Ancestry). Her Probate was at Birmingham dated 28 Mar 1945, National Index of Wills and Administrations, 1858-1957, (FamilySearch).
Augustus Henry Withers. Birth Registration: Aston, 3rd Qtr 1851, Vol 16 P230. Birmingham Daily Post, Saturday 14 September 1889, p5. (British Newspaper Archive). Marriage Registration: Birmingham 1st Qtr 1876 Page 220 Volume 6D Line 45 (Family Search). Death Registration: West Bromwich 3rd Qtr 1908 Page 398 Volume 6B Line 363 (Family Search).
Caroline Rosina Withers. Birth Registration: Aston, 1st Qtr 1853 Vol 6d P271 Line 40 (Ancestry). Marriage Registration: West Bromwich, 1882 4th Qtr Vol 6b p1234 (Ancestry). Death date, 13 Apr 1946, from England and Wales, National Index of Wills and Administrations, 1858-1957, citing Probate, Birmingham, Warwickshire, England (FamilySearch); Age 93, 17 April 1946, St Michael and All Angels, Thursley Surrey, Thu/5/2 (Ancestry).
Walter H Withers. Birth Registration: Aston, 4th Qtr 1854 Vol 6d page 254 Line 15 (FamilySearch). Marriage Registration: West Bromwich, 4th Qtr 1887, Vol 6b p254 (GRO). Death Registration: Victoria Australia, 13 Oct 1914 (Public Records Office, Victoria). Probate; Walter H Withers, 20 Nov 1914; Series 136, record 229 (Public Records Office, Victoria (FamilySearch)).
Charles Ernest Withers. Birth Registration: West Bromwich, 4th Qtr 1856 Vol 6b p518 (Ancestry). Marriage Registration: West Bromwich, 1915 Vol 6b page 1119 (Ancestry). Death Registration: Birmingham, 1942 Vol 6d page 30 (Ancestry).
Any corrections or improvements are most welcome. Especially the Death Registration for Clara Shorten which I have not found.
Thanking you