I'm confused.
Why are you in denial about your children's obviously advanced mental abilities? Would you respond the same way if they were at the other end of the spectrum?
Does the private KG allow potential students to visit for one or a few days? Does it have some kind of transition program for potential new students? If yes, then have your child "try it out." That will give you some solid information about how well the program will work for your child.
Also, remember that pretty much any decision can be changed. It's not all or nothing.
