I now have my own local grid configured at home using OpenSim with MySQL. I've put four (one-region) islands on at the moment, including one for each of my three children. They will be able to walk/fly to each other's island. There's plenty of virtual space though - regions can be placed anywhere on a 65536 by 65536 grid! No (15,000 per region) Linden Lab prim limits either!
My son William (9) had the idea to make a football pitch on his island and a football with physical properties so that it would roll. Unfortunately, it kept rolling off the island, so he terraformed a boundary around the pitch. I wrapped a picture of Mr Bean dressed as a punk around the football. OpenSim was misbehaving and my appearance went a little bananas. The screenshot shows William in the background trying to influence the direction of the ball which is flying off for no apparent reason.
Whilst awaiting "delivery" of Kilburn Island for Computer Science, I decided to download and setup OpenSimulator Standalone (0.5 Rev 3697) at home, the free alternative to land, in its early stages. Each of my three children (9,7,5) now have their own private island with which to experiment! They can get together for building, terraforming etc. on each other's islands (only one visible at a time though), without the lag and age restrictions (13-17,18+) imposed by Linden Lab. My five year old daughter loves terraforming - the visual feedback is instant, and the changes persistent.
The next steps will be to install MySQL and setup my own local grid, so multiple islands can co-exist, and my children can visit each other's islands.