Make a willow house!
Build a geodesic dome!
I'd look at "sustainable" buildings or structures that use recycled materials for inspiration. It'd be a great way to get your kids to learn a little about protecting the environment if their shelter was a cobb hut or built from hay bales or built from concrete and soda bottles. Even if you wanted to get traditional, you can get reclaimed lumber pretty easily these days.
You should also consider taking building a structure that's useful to adults and converting it for the children. For example, you could build a castle tower from a gazebo by adding fake crenalations at the top and enclosing it with plywood walls. After the kids get a bit older, you can remove the modifications and repaint.
Whaterver you chose to do, build a solid structure for your children's safety.