George Edmunds Williams seems a very well to do man, had some standing according to various newspapers of the time.
I wonder if Millborough, having had 2 (on the face of it) illegitimate children used Carlton and invented George Cox on her daughter's baptism in 1839 to make it more respectable when she was Millborough Cox at birth. Maybe Mr Carlton was one of the fathers?
GEW certainly seems to have taken her 1839 daughter on as his own as this daughter names him as her father on her marriage certificate and uses Williams