Tux Paint

There is a configuration tool for parents/teachers, or you can just edit the config file. The right mouse button can be mapped to the left, or to an animation that explains left/right buttons. You can make Tux Paint full-screen. You can disable the normal way to exit, leaving only a non-obvious key sequence. Tux Paint uses a fixed-location save directory, so there is no way to browse around and mess with the OS.