We definitely have two Amadine Booth here, but which one are you interested in?
1. The daughter of James Booth and Sophia nee Smith (as in your thread's title)
or
2 The wife of Naphthali Smith (your direct ancestor's brother)?
I can trace the Amadine w/o Naphthali on 1871, 1881 and 1891 censuses. In 1871 she states her age as 20 and pob Leicester, in 1881 she is age 27 and pob is Gt Peatling, Leics and in 1891 she is age 40, pob Peatling. We should be looking for a birth between about 1849 and 1854 in Leicestershire. But nothing likely comes up on freebmd.
Have you got her marriage cert? If so was she single? If you are only going by the GRO index entry, that will only give name at marriage, she might be a widow (possible reason for the delay in her and Naphthali marrying) and Booth therefore not her maiden name.