Except for moving pieces against the rules, SCID (free chess database) will do what you want, http://scid.sourceforge.net/, and much more that would be useful in teaching chess.
e-Tools for teaching chess

Many ways to get what you want:
The tech-route:
- Laptop with SCID (free chess database app. that does what you asked for)
- Projector
The non-tech route:
- Buy a large demo board from any online chess equipment retailer.

Thanks folks. Yeah, an electronic version of a demo board was kinda what I was going for. Maybe I'll just go low tech. I'll check out SCID.

BTW, I wrote some (free) software I use in a chess club I support: https://sites.google.com/site/fredm/. I frequently use SCID and a projector as Shivsky suggests.
Hi Folks,
I'm a teacher and have recently started a chess club at my school. The students are interested in more than just playing, and so I want to start teaching too. We have smart boards in the classrooms, and so I would like to know if anyone has relatively cheap software or online flash tools for teaching chess.
Preferably I'd like something like the following: A board where I can move all the pieces in any way I'd like, not according to the rules, such as moving the same colour twice, etc., but that also lets me back/forward moves. Also, preferably it would let me set up positions.
Any suggestions?