If you go the tandem route, just add a Child Stoker kit.
Check in the Tandem section of this forum, but I imagine they're capable of being mounted on any tandem. I used one for years with my daughters.
A used low end tandem plus stoker kit shouldn't be cost prohibitive.
You could also look into recumbent trikes. They are so much fun that they are addictive. A tadpole might be a good place to start. back when I used to take my family on camping vacations, almost all the campgrounds had a few available for the kids to play with. They loved them!
check this out.....
http://mnhpva.org/Mini_Bents/Mini.html