Dog not housebroken on rugs

Question
We have a four year old mix breed rescued from the CACC when she was under a year.  She's about 40 pounds and looks like a small German Shepherd.  

I'm at my wits end with her.  She is a nice dog.  We love her.  But she is constantly peeing on the carpets and rugs.  And recently she starting pooping on the floor too.  It's usually in a particular area so I figured that no matter how much I clean, the scent is still there.  I've had them professionally cleaned and that helps for a short time but then she's back to peeing there.  I put stuff on top of the spot so she won't go but them she'll just go somewhere else.  And recently she started going on new carpeting where she'd never gone before so clearly it isn't just a scent thing.

Also, the big problem is that we never seem to catch her.  She'll do it if we leave the room for a moment.  I realize an obvious answer is to never leave her alone but that's not a realistic option.  As it is I am hyper aware of where she is at all times and trying to keep her in my sight.  We tried gates to the rooms that she tended to go it but now she jumps over them.  I tell her NO when I see her doing it but it doesn't seem to help.  She'll do it again as soon as my back is turned.  

It's as if she can't control herself with carpet.  This began when we moved into a new place and put down carpet an rugs (we had none in our old place).

I really don't know what to do.  We love her but I can't live with cleaning up pee and poo all day especially when she's getting out plenty.  Nothing has changed in her life so there's been no trigger.  And she's fine medically.  

I appreciate any advice.  Thanks!

Answer
What I recomend is using a crate-keep the dog in there and just let her out first thing in the morning,just after she eats and every few hours to pee,and put her right back in the crate

Dog will not want to soil there sleeping corners-now after doing this for a couple weeks,just start to put her in the crate at night and when you go out,it might also help to put the crate on the spot that she is messing for a while