You said the cats stay upstairs and the dog down unless the cats want food. Do the cats have to go downstairs and past the dog to get to the basement where their litter is? I would venture to say that is a huge part of the problem. Most likely the whole problem. What a dog does when it's humans are around is not what that same dog does when they are not around to intervene to stop it from being a dog. It is quite possible while you are sleeping at night the dog is terrorizing the kitten. It does not take much to make a small kitty petrified of a larger being, dog or human.
Which leads me to the next part....... rubbing a cat's nose in its pee does nothing but teach it to show fear for the person doing it to him and may possible lead to more issues. The cat has no idea why it's nose was rubbed into the urine. Also the yelling and spanking does no good. The kitten has no idea why it is being hit. The kitten at this age is the equivalent to a 3 or 4 month old human baby in age.
If we look at this from the kitten's point of view we will see it was quite settled and happy in the house and all of a sudden a large animal with the potential to hurt it badly was brought into the picture. The poor kitten has no idea how to react. He is afraid to go to his bathroom because he is afraid of this larger being. So he uses the closest thing he can find that resembles his bathroom. Unfortunately it's your bed.
Are you using something like Nature's Miracle to clean your sheets and mattress? You need to completely get rid of the smell of the kitty's urine. You may think it's gone because you can't smell it but the kitten may still be able to. A mixture of 1/4 cup vinegar, 1/4 cup rubbing alcohol, 1 cup of water mixed in a spray bottle and sprayed liberally on the areas the kitten has peed on will help eliminate the smell.
Assumptions do nothing but make an ass out of u and me.
We can stick our heads in the sand for only so long before it starts choking us. Face it folks. The pet population is bad ALL OVER THE WORLD!