Hi,
Newbie here - I found the site by accident about 3 days ago, and have been glued to it ever since!
Assuming you have read and understood all the forgoing regarding legality.......
I haven't built an Internal Combustion Toylander, but I HAVE built several 'ground up' go-kart type vehicles with I/C engines. The simplest set-up is a Horizontal Crank type engine (suffolk Colt or similar) with centrifugal clutch, driving one rear wheel as per plan.
Better - use it to drive an axle from a small ride-on mower. The axle contains a differential, so both wheels can be driven.
Another option - use a vertical crank engine (MUCH easier to find, and CHEAP). I happen to know a 3.5HP Briggs & Stratton 'Quantum' will fit nicely under the bonnet. Use this to drive a transmission from a ride-on mower (which will incorporate multiple forward gears and a reverse), and which will also turn the drive 90 degrees, then chain drive to an axle as above. Would have to rig a 'belt tension' type clutch, and the transmission can't be 'hot-shifted', but not really a problem, since the gearing is such that the car will pull away in top gear easily. CAREFUL choice of engine needed - must have a heavy flywheel to allow operation without the mower blade. Use an engine from a power washer, or a mower with a blade clutch (which will be useful), to be sure. Surprisingly, some of the cheap, Chinese origin, mowers, have such engines. Briggs, Tecumseh and Honda (among others) have electric start options, and include on-board alternators (puny, but useful).
A hydrostatic transmission from a garden tractor would solve most of the transmission problems, BUT is big and heavy - at least compared with the original electric set-up. As a bonus, however, some garden tractors incorporate hydraulic power steering driven by the transmission pump. This would transfer easily.
Just some thoughts - where I live this would be pointless, as there's NOWHERE it could be legally used, but if you own some private land, or live on a farm, it might be an interesting project.
Regards,
Phil