I can’t tell from your post - are they MAKING the dog live in the mudroom, like closing him in there so he can’t get out? Or is he choosing to be in there on his bed?
My family has had two dogs, both male labs, who were very different in their relationships with us. The first, Max, we got as a puppy, and although he would tolerate playing or petting for a while he always liked his space. Once he had his fill he would get a little growly and then everyone left him alone. There was a chair in the living room that he took over as his own, and most of the time he could be found there. At night he slept there, not with any of the people in their bedrooms, by his own choice. He lived to be 14 years old and while he was a loved family pet, he was this independent sort of way his whole life.
Sam, on the other hand, we got from the shelter at 9 months old. He was part of a litter of puppies that had been kept outside and not properly cared for, so were taken in by the SPCA. He was a velcro dog and always had to be right with someone or at the very least in whatever room the people were in. If you were alone and say went in the bathroom and closed the door, he would wait right in the hall outside. He slept on his own dog bed on the floor in my parents’ bedroom. Sam just passed this fall at age 13.
So, given a choice, I can see a Max-like dog choosing to stay by himself most of the time. A Sam-like dog, on the other hand, would probably be sad, anxious, etc if not with his people.