Dog hiding and peeing

Question
We have a female lab who is about 7 years old.  We got her 2 years ago (previous owners were getting a divorce and couldn't take her with them), and have had trouble with her hiding in the house to pee.  She's taken out frequently, and we have never been able to catch her in the act.  We first noticed it at our old house in the finished basement, but I thought maybe she was smelling where one of the kids had had an accident on the carpet.  It got to the point we couldn't stand being in the basement because of the smell, and no amount of cleaning the carpet helped.

Now we're in a new place, and she is continuing to do this, only now it's upstairs which is a 2nd floor attic turned in to a bedroom.  It's mostly around the top of the stairs.  We've tried keeping the door locked, but it's almost like she waits for one of the kids to leave the door open so she can go up there and pee.

We are at our wits end with her!  We have thought about taking some of electric fence wiring and putting it at the top of the stairs to scare her from going up there, but I'm afraid she'll just find another place to pee.  Plus, my son likes to have her sleep up there with him.  I just can't afford to keep replacing carpet, and I can't catch her in the act to stop it.  In both houses, these were the only spots she peed, so I know it's not accidents.  She does it both while we home and while we're gone if the door is left open.  I know for a fact the previous house didn't have a history of dogs peeing because it was newly remodeled, so she's not peeing over another dog's smell.  We're seriously on the verge of getting rid of her because she's destroying the house.  Please help!

Answer
Since she's eliminating at the top of the stairs, she may very well be assuming this is OUTSIDE the "den" (sleeping area).  This dog might very well have been seriously punished for urinating indoors as a puppy and her house training skills may not have been successfully put into place.  A dog that sneaks around to urinate is usually working off a strong conditioned fear response; such a dog might not urinate in front of you outdoors, even when a reward is introduced (initially) because of this fear.  Imagine not being able to go to the bathroom without being fearful!  She might also be demonstrating a physiological problem!  A veterinary check is absolutely necessary.  There are all sorts of conditions that provoke urination (even when the dog has been let out and done the job there.)  She needs a checkup and a blood chemistry to rule out illness.

There are dog diapers available in every pet store which do a wonderful job of containing the urine and change the behavior, since the urine does not leave proximity to the dog's body and the dog quickly learns not to urinate when wearing the diaper.  Some dogs will attempt to remove the diaper, others will seemingly ignore it.  If it's introduced with an associated reward, the dog might more easily accept it.  Providing your dog WILL eliminate outdoors in your sight, go out with her and reintroduce appropriate elimination with good (small) food reward.  Do this for at least three weeks, during which time she must be prevented from urinating indoors.  She must not be allowed free access to any area she has already marked, regardless of the inconvenience to you.  Doors must be kept closed; the dog must be kept on a long house tab (training leash, up to 16 feet) so she cannot slip away; and her sleeping area has to be changed.  This is a living creature who is depending on you for her safety.  Your son can learn to live without her sleeping in his room, but NO ONE is going to take a 7 year old dog with a house training problem.  She will be PUT TO DEATH at any municipal shelter, while suffering extreme anxiety at her abandonment.  And this is not a wonderful message to give to your young children, either.

Confine her; restrain her on house tab; reintroduce house training with reward; show patience and kindness.  Your children are watching.