The brief answer to this is that the family decided to live in their cave for the rainy season. They decided to call the cave "Rockburg." You can find this name, along with a description of what they did during the rainy season, in Chapter 10.
The family chose to live in the cave during the rainy season because it was, by far, the best of their homes for bad weather. Falconhurst, for example, was very uncomfortable in the wind and the rain because they were not able to keep the rain out of their living spaces. By contrast, they were able to make the cave quite weatherproof. They also got the cave all set up with lots of things to do. They set up a forge. They had a large library of books. The books, for example, helped them to pass their first rainy season in the cave by learning various languages.
So, the family chose to live in Rockburg during the rainy season because it was weatherproof but yet had enough things to do to keep them busy.