I'm not an Emerson relative (well, being a fellow Kiwi, I could be, but as far as I know it would be very distant lol), but I would definitely say that these four records all relate to the same person.
The marriage record in Derbyshire is notable because, on the 1861 census, the eldest of their children is listed as being born in Derby, and based on the age estimate for the son he would have been born about a year after the marriage, which was fairly common in the nineteenth century because the mindset was that you married in order to have a family.
I also think that the 1871 census is likely correct, so long as there is no other George and Georgina in the area. Censuses often record the children as being from the same location as the rest of the family, whether out of laziness or convenience I can't say, so it's certainly not even close to being unheard of to find a child in a family listed with an incorrect birth location.
Similarly, with the 1911 census, I'd say that its probable that its the same George so long as you cannot find another George born around the same time, in the same place, which fits the bill better. This George is listed as a widower, so Georgina has to have passed away between 1871 and 1911. I couldn't find any death in the GRO; all of the deaths I found for the name Georgina Emmerson did not even close fit the age that she would be, which is why I'd take more caution with that record but it certainly isn't out of the question.
