Gillian,
I'm getting very confused

In your third sentence, did you actually mean
marriage rather than
birth certificate? If you have Priscilla's birth cert, then you
know what her maiden name was! But, if you do mean birth cert, what were the names of her parents?
Also, you say that you have found a marriage for a William THOMAS and a Priscilla THOMAS in 1867 in Leeds. I can't find it on FreeBMD (there's a William THOMAS at the reference you gave but no Priscilla - but we know that FreeBMD is incomplete). If that's the case, then it seems quite likely that THOMAS might have been both the maiden and a married name (from a previous marriage) of the Priscilla who married James SKIPSEY.
Precisely what does it say on the 1874 marriage cert?
Is Priscilla recorded as a spinster or a widow? (Remember, she might not have told the truth! If William THOMAS was her first husband, she might not have told James that she'd been married previously - which would have been easier if her maiden name and the name of her first husband were the same! And there's always the possibility that William was still alive ...)
What is her father's name and occupation on the marriage cert?
And on the 1871 census (if you don't have the details, you could post a request for a lookup for this and also for 1861) was Priscilla recorded as Henrietta's daughter?
Incidentally, there's a death for a Henrietta THOMAS, age 66, in Leeds, Jun quarter 1875.
Whatever it is you really are trying to find out might be able to be sorted out here. Otherwise, I'd suspect you'd have to purchase (say) Fanny THOMAS's birth certificate or the cert for the 1867 marriage between (you say) William THOMAS & Priscilla THOMAS.
If Priscilla is recorded as Henrietta's daughter in 1871, it is interesting that James & Priscilla SKIPSEY named their first daughter Henrietta ...
Good luck,
JAP