dog's house would be like saying it was the dog's house, it was the dogs possesion so you would have the '. and then dog house means its no one's and its just a dog house.. like if i were to say... " wow look at that dog house! ".

There is an expression "you are in the dog house" meaning you did something very wrong and you are now in disgrace. The dog's house seems to me to be just the house of the dog :)