Mammoth Cave National Park

Agree with other replies - one cave a day is plenty and at that age the 3rd cave will be the same as the first two unless there is something significantly different between them. Jellystone Parks are perfect for kids and serves as a good balance against the "educational" dimension of the caves. Kids need time to have fun, too.

Our kids were 3,7 and 9 when we visited. Depending on your ages and ability, you could easily do one large tour and be done. I don't remember the name of the tour, but there's one that's three hours long and starts right behind the visitor center, that was perfect. It included frozen niagara, large open spaces, and tight spaces.
We stayed at Jellystone and we liked it. The kids enjoyed the action park right outside of the entrance to the campground. There's an alpine slide there they enjoyed.
Have fun.

We have been there three times. With that age children, one cave tour would probably be enough. Unless you want to do the "general" tour, I would recommend you make reservations. If Jellystone is unavailable, I recommend Dog Creek COE campground. You can take the back way into the park on the Green River ferry.

I'd say minimum of 3 days.... one cave tour a day is probably enough as it can be strenuous depending on the tour(s) you select. Jellystone has lots of activities for the kids too.

We stayed 2 nights and enjoyed it very much, years ago.

There are many other caves to tour besides the NP. Cub Run Cave was our favorite.