Peeing on dog bed

Question
Six weeks ago we adopted two bonded purebred female labs from local shelter, picked up as strays, 1-1/2 yrs old, spayed upon adoption.  Vet feels they are siblings.  They behave wonderfully and train easily except one or both pee on their bed(s) at night.  This didn't happen as often at first, but now it's every night.  They have 3 fenced acres to run freely during the day, and come in the house at dark for the night.  We take them out to pee just before we go to bed.  Even if we take them out again at 5:00 a.m. they have already peed.  The other night one peed on her bed just after she'd been out.  We have them sleep closed up in our laundry room, otherwise we find them on the sofa in the morning - hmmm no pee then.  They never have peed in the house when we're up with them, even if it's for long periods of time.  We have not punished them for this as it would seem to be psycological.

Answer
Because these dogs are so closely bonded (a pack) and likely siblings, this appears to be a rank related behavior, which means they are very close in temperament and one is marking the bed to make a statement to the other (possibly marking BOTH to make a statement!)  Determining which one is the most dominant in temperament is your job, and then treating her as the "top dog" should help eliminate this situation.  You must closely observe these dogs in interaction with one another AND with you.  Who comes to you first (or bumps the other one out of the way to get there?)  Who gets to the door first (or bullies the other one out of the way to get there?)  Who "wins" the toys when they play (keeps them, hoards them, removes them?)  Who gets to the food bowls first?  Even though they are very close in temperament, ONE of them is naturally a bit more dominant than the other.  Observe tail set (high over the back is dominant, mid-body height is friendly, tucked low is fearful or subdominant); observe ear set (perked and forward is dominant; relaxed is friendly; wrapped back is fearful or subdominant.)  Observe facial expression (the Lab is very expressive and shows worry, happiness, fear, etc. easily).  Observe hackles (raised is excitable or dominant or fearful.)  Observe their eyes: lots of white showing is a sign of subdominance or fear.  What are these two dogs SAYING TO ONE ANOTHER?  Read Turid Rugas' book on calming signals, this will help you determine their language.  Then, when you are certain who is who in this relationship, promote that one psychologically.  You do this by feeding her first, greeting her first, letting her in/out first...in other words, treating her with a tad more "respect" than the other.  The possibility that outright aggression between these two female dogs will develop as they mature is a problem unless you counteract it.

While determining which dog is higher ranking, use positive reinforcement training to teach each dog (separate from the other) some simple obedience tricks (like sit, down, etc.) using words that are different from ordinary (in other words, not sit or down.)  Then use those skills to make BOTH dogs work for YOU.  Make them work for their food, for being played with, being let in/out, by asking them both to do a simple behavior like 'sit'.  This establishes your rank over both of them in a kind and rewarding manner.