Any vertical shaft domestic engine can be fitted
Only another Kohler will be plug & play .
Unless the crank case has developed a crack in it from not checking the closure plate bolts of the counter weight punching through the crank case there is little else that goes wrong with them that would warrant replacement .
The surplus engine vendors usually have tons of brand new engines at near 1/2 price .
SEW
SES
TSC
All good places to look
Secondly a ride on mower is not a toy for the kids to play with
It is a dangerous piece of kit that injurs thousands of careless owners and their children every year.
Riding two up with the kids is not going to reinforce how dangerous a mower is .
A blade belt will take a childs fit right off in such a mangled mannar it can not be replaced , let alone contact with a blade