First of all, when there is not a room available, what is the owner supposed to do? Kick out someone else?
Second...if this is a mistranslation, what else is “mistranslated?” You are going to get some “word of God” folks upset at that! Ha ha.
Not a mistranslation, more of a generous use of the word. The Greek is "katalymati" and referred to a place to stay after a long journey. Similar word is used in Luke 22:11 "katalyma" as "guest" or "upper" room. 1st Century Judea had dual purpose homes where the upper room was for guests and the lower room was where the family and the animals slept (for those who owned some animals). Not every house had this, but some on the edge of an established town.
Summation: an upper room that would be rented out to sojourners, aka "inn".
Jesus was born in a barn and laid in a manger because it was GOD’S PLAN that He be born in a barn and laid in a manger!