Alan, I'm thinking Emma is right. Each install of Moodle should have its own data directory. The easy installs from cpanel can sometimes point to the same data directory as it is a scripted install.
Thank you for your interest in Pioneer and Fordson. I don't believe the themes are the root of the issues your experiencing.
Create a new folder next to the current Moodlesite folder. Edit one of the Moodle config.php file to utilize the new data folder. Make sure www can read and write to your folders.
That should fix the issue of shared data folders.