That night in Bethlehem

It was a troubled era.  Joseph may have easily saved Mary's life by taking her (despite her condition) with him to the census--zealotry was born at the same time people were calling for the Messiah, and persecutions were growing.  

In this part of the world, many homes were caverns or homes built into rock, sharing space for humans and animals alike.  There is no knowing if this is the case for Mary and Joseph, but there was no shame in making a cradle out of the manger--in those days they tended to be made of cut stone and weren't likely to tip over!