Hah - your son will totally love it. There were quite a few kids and even a school bus (despite spring break) there. There are also little activities like 'washing for gold' and rock splitting to find ore. It's a great place to spend a couple of hours and learn about history.
I get your wife, I don't like tight, enclosed spaces e.g. elevators. But this was really fine, the walk didn't go too far into the mountain - it felt okay.