This chapter starts about three months after the first, or at least very close to Mary's due date. It picks up with the order from Caesar Augustus (Octavian!) for everyone to register. (And thus the confluence of book and history-crush!)
Joseph has trouble deciding how to register Mary. He doesn't want to register her as his wife, because technically she isn't, totally. Remember? He considers registering her as his daughter (which is another indication that Joseph is a good bit older than Mary), but knows that all of Israel will know she isn't his daughter. He decides to leave the decision in God's hands, saying that "This is the day the Lord has made; it will turn out as he wills." So he's decided not to make a decision.
So he saddles up a donkey, puts Mary on it and heads out with one of his sons leading the donkey. The make it three miles when Joseph glances back at Mary and sees that she looks very, very sad. He wonders if maybe the baby is causing her pain. But then the next time he turns to look, she's laughing. So he goes back to her and asks how she's doing. Mary replies that she's seeing two peoples in front of her, one afflicted and grieving and one joyful and exulting.
The author's note says that the two peoples in Mary's vision are traditionally understood to be two branches of the Jewish people. The ones who are grieving are those who rejected Christ and the ones rejoicing those who accepted Him. The later includes those Gentiles who believed in Jesus through the preaching of the Apostles and were grafted into the 'tree'.
When they were half way to Bethlehem Mary told Joseph to help her down off of the donkey, because 'that which is within me presses me to come forth.' He takes her down off of the donkey and asks her, 'Where shall I take you, to cover your shame? For this is a desert place?'
The author makes it clear that shame is used here as a euphemism for 'private parts'. Though I dislike the implications in using such a word for any part of the human body, it is historically accurate and well, it's hard to judge history by our modern standards. We just shouldn't do it. I think Joseph is basically just trying to find Mary some privacy from any wandering travellers because giving birth is one of those things you don't really want any random stranger to see. No one looks good giving birth. I've seen it, and it's Not. Pretty. Also, babies are ugly and squashy when they come out. And sticky. Giving birth is a miracle of life, but it's a messy one.