Kids have to mature, as do we. The first step is to trust your kids and let them go. It is much easier said than done, but you gotta do what you gotta do.
In terms of travel, your kids are at a great age to start training. I had mine learn how to make online bookings, get boarding passes, look for schedule updates, go to gates, etc. You can watch them from behind and allow them to be confused a little. Once they figure it out, it’s a great feeling for the kids and parents. You should also have them learn about subway and bus maps at some point, because kids will have to use them sooner or later.
Good luck and let us know what schools you decide on applying to. You will find a lot of good advice here!