I kind of get you OP. If the father is not named on deeds or a rental agreement then he doesn't really have a "home" of his own. He is a resident, as a PP pointed out.
But I do take issue with some of the responses saying that where one lives is one's home, and automatically one's children's home. "Home" to me is more of a feeling than a place, and having been a stepchild, it can most definitely NOT be the case that your father's home is your home.
Although my father re-married (the OW) and they (presumably) had joint names on their rental, it never felt like home to my sister and me. We were guests. We perched on the edge of the sofa, were given tea in a china cup and saucer along with a dainty little sandwich, and we were talked at. It was made very clear to us by the OW that a great deal of upheaval happened to allow us to stay overnight, and there was never any suggestion that we were actually welcome, or could have or own space, or any of the things that constitute a home. We were just visiting our dad, and staying over for a couple of nights.
Dad would often say that he wanted us to think of this as our second home, but we knew instinctively that his wife didn't share that view. But guess what? It didn't bother us. We knew where home was. It was with our mum. This was just something to be endured because we were sent there due to the access order, but it was never home.
Children aren't dumb. They know the difference between a house and home, and only they can decide where "home" is.