The phrase you picked up as “Your one” is probably better written as “Yer Wan”
It's used to indicate a woman the speaker is referring to.
With such a translation as "the women" however much of the speakers meaning is lost.
The phrase does a lot more than just identify the women. It also shows a certain contempt for her on the speakers part, or also their surprise or shock about what she did or said in the current scenario.
A very similar phrase we also use is "Yer woman"
Usage of this phrase doesn’t carry the same contempt as does “yer wan” and so is used to refer to a woman in informal speech or telling stories etc. Why we can’t just say “the woman” in this case I do not know!
Maybe Irish people just like to give English a bit of an Irish twist!
I've been trying to think of when you'd use "yer wan" and have concluded that it is Irish men and not women that most frequently use it- surprise surprise!
Anyways I did manage to come up with this example and I hope it illustrates my explanation effectively:
“Women don’t know how to keep their noses out of every elses' business. I was down at the pub the other night and ended up walking home after yer wan behind the bar took my keys off me.”
As for "pulling the piss". I can only remember it becoming popularly used from the nineties onwards and would think its just a combination or "taking the piss" and "pulling my leg", slang phrases that originated in England and
pretty much mean "You're joking right?"
We really just made "pulling my leg" vulgar I guess! That is perhaps key to the Irish twist on language :)
Hope this helps.