I've found George Rotton in the 1861 and 1871 censuses, where the information matches what you've found.
1861: Vine Inn, 33 St George Street
George age 42, retail brewer and gun finisher
Sophia age 40, his wife
6 sons: George 18, Henry 16, James 10, Hammond 8, Thomas 6, Walter 7 months. The eldest two are also gun finishers.
All born in Birmingham.
1871: Lamp Tavern, 33 Cannon Street
George age 52, licensed victualler [= publican]
Sophia 50
son George 28, licensed victualler's assistant
son Hammond 17, jeweller
son Arthur 2
daughter-in-law Julia 27
granddaughter Nellie 3
A later rate book confirms that Julia is the wife of George Jr and not one of the other brothers. The "son" Arthur aged 2 seems unlikely (Sophia would have been 48). I suspect he is probably George Jr's and Julia's son but the enumerator got their wires crossed.
I also found George Sr's baptism record; he was born 10 Dec 1818 and baptised 8 Mar 1819 at St Philip's church, Birmingham, son of William and Amelia of Lichfield Street. William is a mathematical instrument maker.
I can't find when he married Sophia, but they are living together in 1841 on York Street, and he is a gun finisher.
I found a directory (which you may already be aware of) - 1858 Dix's Directory, where George is a retail brewer at 33 St George's Street.
He died on 5 Nov 1876 at Cannon Street and his will was proved 23 Mar 1877 at under £3,000.