Bit confused OP in your previous post you mentioned one dog, now sounds as if more than one and both with problems. Have you checked that they don't have an illness? If they're defecating indoors it could be a parasite. My younger dog, who we adopted when she was a few months old did this, and turned out had Giardia which the vet treated.
As for the snip it won't automatically house-train your rescue dog, and it may be that your rescue dog is afraid to go out alone at night, my older ,smaller dog didn't like the noises at night - cats/foxes etc...we always went out with him if it was the middle of the night. He may also, like many dogs, dislike being left alone at night, again dogs vary, my older dog disliked sleeping alone, my younger not that bothered.
But Biteyshark's suggestions on the other thread are very sensible, and comparing with other dogs is really not worth your time. Dogs vary and this is a small dog in a new situation, it also sounds as if you are stressed about the smell and that will also be communicated to your dog and anxiety does not help with settling. You need to house train from scratch, and spend time bonding with the dog. But you do need to try to chill out more about the smell, if you've had dogs before then you will have had or should know that you can expect accidents, stomach bugs, vomiting and other forms of fluids as par for the course. And when they're older incontinence or accidents because of mobility problems are common. You should also bear in mind that urination is a form of territory marking that can make anxious dogs feel safe, so it may be that the dog is doing this because he's nervous or anxious at night.
While you're training get some decent anti-bacterial pet cleaning spray from Pets at Home or similar which will contain enzymes to cover up the smell so the dog can't smell it either.