The census returns provide the following clues to their existence:
Elizabeth 1861 (age 4) born Uckfield
Elizabeth 1871 (age 14) born Uckfield
Eliza 1871 (age 5) born Uckfield (should have been Brighton)
Elizabeth 1881 (age 26) born Uckfield working as a cook
Eliza 1881 (age 14) born Uckfield (should have been Brighton)
Elizabeth 1891 (age 35) born Uckfield working as a cook
Eliza 1891 (age 25) born Uckfield working as a housemaid in Brighton
Elizabeth 1901 (age 47) born Uckfield working as a cook
Eliza 1901 (age 35) born Uckfield married to John Smith in Newick
Elizabeth 1911 (age 54) born Uckfield (pensioner)
Eliza 1911 (age 42) born Uckfield married to John Smith in Newick
Elizabeth 1935 (age 78) died in Uckfield
Eliza 1944 (age 78) died in Newick
It is clear that there were two Elizabeth's because they are both in the same household with Sophia in 1871 and both identified as her daughters while George's children are identified as in-laws which was used for step children. There are no deaths registered for either Elizabeth DAWES or Eliza DAWES between 1881 and 1901 nor is there a marriage so what happened to her?
The trail of these two Elizabeth's is a good example of the many pitfalls that genealogy researchers can fall into. When Eliza disappeared in 1891 it was because she used her middle name "Emily" on the census. It wasn't until seeing her marriage certificate (above) that her full name was confirmed as Eliza Emily DAWES. In 1901 and 1911 she reverts to using only Eliza but she has been found which is the main thing.
Similarly, Elizabeth b. 1856, was hard to find in 1911 until a search for only people named "Elizabeth" and born about 1856 in Uckfield turned her up as Elizabeth DAVIES, a common mis-transcription of DAWES. The fact that she is living with her mother, Sophia, b. 1831 in Cranbrook, Kent proves who she really is.
The final episode in this story will be to find the death of Eliza SMITH, sometime after 1911, and to determine if her daughter, Ellen SMITH b. 1904, married and had a family but that's for another day.
(UPDATE Sep 20, 2009) I found a death for an Eliza E SMITH (age 78) registered in Lewes in 1944 March Quarter Vol. 2b Page 269. It will not be conclusive without a death certificate but with the middle initial E, correct age and location it is good enough for me.
Also using the GRO indexes I have found a marriage for Ellen SMITH to Harry E. MOORE registered in Lewes June Quarter Vol. 2b Page 408 followed by two births of Moores with a Smith mother: Joan M. MOORE 1926 Dec Quarter Vol. 2b Page 213 and John E. O. MOORE 1928 Sept Quarter Vol. 2b Page 215 both also in Lewes Registration District.