May I ask how long she's been peeing laying down (has she always done this)? Does she pee only in her sleep (IE: the urge to pee is not waking her up) or does she pee laying down even if she's awake?
Have you asked your veterinarian about this behavior to see what he/she suggests?
How long did she have her UTI? If it went untreated for too long, it can cause scarring in the bladder, which would cause it to be unable to hold urine as a healthy bladder would...signs of this are peeing in strange positions and places...they have a hard time holding it.
This is a useful read:
Urinary Incontinence in Dogs: Causes, Treatments
The only way to find a definitive answer is to take her to the vet and demand answers.
