I am sure that Abdu'l-Baha thought of his family countless times, while he was traveling across the United States. He certainly thought about his family on April 29, 1912. That was the 9th day of the 12 day long Ridvan festival.
Abdu'l-Baha would have remembered what happened on the 9th day of that first Ridvan. That was the day when Abdu'l-Baha and the rest of his family joined his father, a man who had been living in a garden. The family moved out of their house, in order to prepare for their trip. The family set out on their trip on the 12th day of Ridvan.
The first, 9th and 12th days of Ridvan are now celebrated by Baha'is throughout the world.