Same problem here with Bunnie with crystals in her urine. She leaked when she was laying down and also squatted to pee on one of our rugs (brand new, of course).

As for the stretching, that can be a sign of pain.

Try and get a sample up to the vet - a quick litmus test will determine what the problem is, usually.

Good luck x

An amusing tale:

We got puppy Dido when my youngest daughter was 11. They were inseparable and when my daughter was home Dido was her constant shadow. When Dido was 12 months old my daughter had a sleepover party for her 12th birthday and about half a dozen little girls duly turned up and took over the living room with sleeping bags, dvds and other required paraphernalia. Unfortunately this did not include one young german shepherd dog. Poor Dido sat outside the living room door (firmly closed) and cried and knocked but was resolutely ignored. I'm not sure what happened next but the first we were aware of it was when the sounds of girly screaming reached our ears -Dido had got into the room squatted down in the middle of the floor and proceeded to poo. We arrived on the scene as she was leaving the room with some great dignity, point having clearly been made.