The second smaller set of wheels look like they may be Wheeleez brand wheels, in which case adapters are available to solidly attach them to a live axle. Then the live axle could have a sprocket which attaches to a gear motor with a chain.
We have helped dozens of people build beach wagons that have Wheeleez wheels so that is something we are very familiar with.
We have many beach wagon kits which would work for your project. Here is a link to them:
We can also make a new kit specifically for your project. If you are interested in this then we could begin with the diameter of the wheels to figure out the gear ratio and sprocket sizes.
I'm looking to add a motor, gears & battery to provide a boost to move beach wheels like this carrying a 400# catamaran. It would be best to install midway between the wheels. It does not need to be waterproof since the wheels can stay out of the water. Any ideas on how to mount and power the drive would be appreciated - Robert