The Flying House was mentioned numerous times in Rome's Revolution and was Rei and Rome's primary residence for their long journey from Tabit to Deucado as they towed Rei's Ark II toward its new home world. It played a pivotal role during most of the book and comes to the end of its useful life at the end of that when it is taken away by the Vuduri.
I thought I'd give you a few details about the craft since not everything was spelled out in the book. The Flying House was one of the Vuduri space tugs converted into living quarters. The interior was rebuilt to make it like a small apartment, reminiscent of a mobile home.
The Vuduri space tug was patterned after the Space Shuttle both in dimensions as well as general appearance. Here is a picture: