Inside I use a 2 mm gray cardboard brace to stabilize the whole thing, tabs are placed all around ...
... on which the sub-floor rests
Now to the wheels, which of course have to be modified due to my changes ...
... cover the halved wheel disks with 0.4 mm cardboard, glue the profile over it
Thus, the wheels should be stable enough to survive the tough game of a three-year-old
Sincerely
Kurt