Red,
we have had exactly the same problem.
Got a boy and a girl. The boy is faultless and goes in his litter tray even cries to get to it if the door is shut and he can't get to it.
The girl will wet anywhere and everywhere. We have TRIED EVERYTHING and she will still do it if left alone.
We have tried sprays, different litter, different litter trays, additional litter trays, putting the litter tray where she has gone (she will then just go in the corner next to the litter tray), putting their food where she has gone, putting citric sprays and fresh lemons down, praising her when she is in the litter tray to make it a good place to go. You name it we have tried it.
But she still does it if she is out of our site and near where she has soiled before.
She has even peed on our leather sofa, while we were stroking her
We tried confining her to the downstairs utility room with a litter tray, she now only goes outside to toilet, she wont go in her tray at all, just think she hates litter trays. We have noticed that she doesn't cover her excretions like our other cat, she just squats and runs.
good luck in finding a solution, it may just be the fact that that is the way she is, that is the conclusion that we have come to.
Also, there has been no disruptions in the house.