I think you may be setting yourself an extremely difficult project here, if you're only after the journey of building a 3d printer and designing one yourself thats fantastic. But I wonder how much of the research and interest your kids will show in the project if and when things go awry, because they will numerous times.
Never ever has a design project been undertaken without road bumps.
But the point I would like to make is this, a good working 3D printer is a technical work of art, if there is any deviation in the frame/airflow/linear rails/vibrations/movement the print product quality is decreased dramatically. Wood warps, how good are your tools? How accurate is your machining capabilities etc, dont want to sound like a hard nut, but im just being realistic seeing as though your kids expectations are involved here as well.
Don't get me wrong its something I would love to do also (designing my own), but the extra drama of the kids being on for the ride of such a complicated first project is out of my own comfort zone.
Advice, as a parent and a technician/manufacturing engineer with 12 yrs experience, buy a well reviewed pre-machined kit andbuild it with your kids and explain the processes and what things do, how they work, why A goes into B, and build their knowledge as well as your own, give them a feel for the experience of building something and designing a project then branch off into other projects using your known respectable working 3D printer to assist OTHER projects/designing your own 3D printer/mill/lathe/router etc.
Sorry, if this is more negative then I intend it to be.
If you are in the UK I would recommend, these guys at Ooznest, they helped me with a project I did not too long ago building an automatic wire cutter using linear actuator rails to mount a cutting blade to cut wires to specific lengths in a manufacturing environment.
I think they are a retailer for OpenBuild products, but cannot say for sure.
One thing to mention however, I wouldn't buy the stepper motor shields from them as they use uStepper boards, reasoning being although they are great motor shields there is not a great deal of documentation or examples about on the internet, should you need help.
Whereas EasyDriver boards by Sparkfun and the Pololu drivers are much more common.