With those details, your story becomes much more realistic, especially for those in here for the $.
The illusion of profitable nuclear power is harmful for the debate. Thankfully you introduced it as fiction.
Neighbor's backyard.
> where does he get the fuel and for how long?
From the Libyans, until they find him.
What makes this utter fiction, would be getting approval from the various government agencies to transport the reactor to his home. Also getting a rail spur into his back yard. Then getting approval to turn it on.
In addition, it would be the equivalent of transporting a fully fueled Falcon 9 to your house... Small is relative! Then the transport out would be even worse because nuclear waste is even more regulated.