Mary and Joseph traveled from Nazareth to Bethlehem for the census or to be taxed, or taxed and counted, but were turned away from the village inn by the innkeeper. They took refuge in a barn, where baby Jesus was born and laid in a manger. A very early church tradition says the site of the nativity was a cave near Bethlehem.
The Biblical story of the birth of Jesus is found primarily in Luke 2. Luke neither quotes nor mentions an innkeeper. We suggest the story does not refer to an inn, a cave or even a barn, but rather a house. Probably.
The text of Luke 2 notes there was no room for Mary and Joseph in the “inn.” Unfortunately, the Greek term translated inn (kataluma) had multiple meanings, among them inn or caravansary. Used only one other time in the New Testament (Luke 22:11 and the parallel passage, Mark 14:14), it was the place where Jesus observed the Last Supper with His disciples. Here, Luke gave additional information about the kataluma. He said it was a furnished large upper story room within a private Jerusalem house. The kataluma of the last night of Jesus' earthly ministry was the “upper room.”
We suggest the kataluma of Jesus' first night was a similar room in Bethlehem. Mary and Joseph came into town with Mary ready to deliver. Arriving at Joseph's ancestral home, they found it already full of other family members who had arrived earlier. While the exact reason space was not made for a pregnant woman is unknown, but one can only assume that Joseph's uncles and brothers were just dicks.
Just to be clear, Mary and Joseph (probably) never went to the barn. The Biblical account mentions neither barn nor cave—it is assumed because of the manger. Mangers are animal feeding troughs, and barns are where one would expect to find them. But in the ancient world, as well as in primitive modern cultures, mangers are also found within the house itself. Animals are regularly kept in homes at night. I will remind you that there could have been wolves, bandits, or just lack of internet porn... Hey, for whatever reason, that's their deal!
Excavations in Israel have uncovered numerous installations within domestic structures which probably represent ancient mangers. Some are carved, but most are stone built.
Consequently, Mary and Joseph did not find space in the living quarters of the ancestral family home. Instead, they stayed downstairs in the domestic stable, still within the ancestral home, where a manger or two was located.
If, however, it was a Travelodge that denied a pregnant Jewish woman to stay there, I can assure you that you would not want to be on the other end of the customer service discussion.