...one window, the main one in our living room, didn’t have a candle until Christmas Eve, when we would put a real, lit candle by it.
That was a candle, Mom and Dad explained, for the Blessed Virgin Mary and Saint Joseph, looking for a place to stay that holy night more than 2,000 years ago. Mary and Joseph — the Mother of God and her spouse most chaste — had to wander the earth, the tradition goes, looking for a haven in which to stay. There was no room at the inn in Bethlehem for them, and they were forced to find shelter in a barn, little more than a cave, really, for Mary to give birth to Jesus, the Son of God, the Savior of the World....
Perhaps the Cardinal had a couple extra doses of Irish whiskey before he wrote that because it does not correspond with what ANY Gospel tells us. In the telling of the Gospels, the journey to Bethlehem was straightforward, but since the town was over-run with registrants for the census, they found a convenient--albeit not ideal--spot for childbirth.
Sure, the Holy Family had to skedaddle to Egypt--much later--because the Son of God was at grave risk of being executed by the local Roman authority.
It's possible that some ancient Irish bard 'enhanced' the story and Cdl. Dolan simply repeated what he'd heard.