There appear to be several errors in your findings The Hon John Salmon 1797-1879=Frances Charlotte Cooper c1819 probably in Jamaica and had 8 children including John Stokes Salmon born 21 June 1821. John Stokes Salmon married Fanny Bush 22 April 1847 and they had the 5 children that you list. They were not the children of Hon John Salmon and Emily.
The Hon John Salmon's second wife was Emily Margaret Senior who he married c 1850. Emily was born 16 May 1830.