If I understand the logic, you have
Mary Letchford daughter of Henry & Mary snr, baptised Derby St Werburgh 1871, untraced in 1881 census, reappears in 1891 near but not with Henry & Mary snr. Then no further trace. No death and no marriage.
1881 census (you don't quote this explicitly but I assume you have it) gives Mabel associated with Henry & Mary snr, Harry, and Rose. Also a baptism for Mabel in IGI, but patron submitted and no source quoted.
In early 1901 Constance Florence appears. No traceable earlier record, either baptism or census. Father given as John, but no other record of him has been found.
1901 has in same house, but different households, Constance Florence and Mabel, plus also Ruth who was born in same town as Mabel.
Finally Constance seems to have been known as Mary.
I think we each have our own standard of proof that we wish to work to. I'd judge it very likely that Constance is Mary. In a way the fact that John Letchford also seems to be an invention supports this theory. I would still though want to explore every possible avenue to see if there is any other cross-check.
The only other lines of enquiry I can think of are:
whether Henry left a will?
the informant on Henry's death certificate
a bit more tenuous, but what part of Derby did she move back to in 1911?
any link to the family's earlier life there?
Did any other Letchfords also move back to Derby?
I suspect though none of this will add anything. In those circumstances I think I'd run with the view that Mary and Constance are the same, but would document very carefully why I'd taken that view.