Unfortunately, I am software engineer, and making one from a custom case, RPi, etc is not an option.
I'm terms of hackabilty, I mean, it will depend on the kids. I try to explain to my kids what is going on inside the laptop and show them it is not magical, but their attention is fleeting. I let my two year play with the screw driver and my 6 year old actually pull ram and replace battery. He likes the old games and has stretched his reading/planning skills to get through Pokemon Red.
Anyways, here is where I frequently find cheap machines.