The best answer to a dispute is to solve the problem. So I've tried to do that.
The Jane Jones seems OK. In Hereford in 1846. The first son Edward was born about 1847 in Hereford according to the 1861 census.
1861 has Edward born 1819 in Portsea and Jane born 1831 in Gosport. If that is correct then she was 15 when married which might acccount for being in Hereford. Although the 1861 census is in Bath, the other children were born in Middlesex. This has all the classic signs of movement of someone connected with railway building.
I can find no death of a Jane Schmidt before 1861 and so a remarriage seems unlikely. I think Jane died in Tonbridge in 1918.
The three are in Westminster St James in 1851. This is the same Jane born Gosport 1831. The census was 30th March, so the January marriage is impossible. Unless it was bigamy!
Incidentally, Edward was christened 1818 RC in Portsea. Father - Joannis Thomae Schmidt Mother Caroletae Murray. Jane is also in Familysearch.
The 1911 census does confuse the issue. Jane is married but husband is nit there. She claims 61 years of marriage! but I'm prepared to believe that that is a mistake.
1901 Jane is a widow. 1891 married but no husband. 1881 ditto. 1871 Edward and Jane. Since she went into service in 1881, it seems likely that Edward died between 71 & 81.
I've put a reference to this answer in Edward's profile.
Also add in Thomas Schmidt marriage to Charlotte Murray here