Frank Lloyd Wright’s Fallingwater has a strict no children under six policy. This applies even to small babies that can be carried in a carrier attached to the parent. If you are going to Fallingwater alone with a child, you are out of luck. If you have two adults in your group, you’ll need to take turns going on the tour, while one stays back with the child/children. This is time consuming (and makes it difficult to see both Fallingwater and Kentuck Knob in the same day) but is doable.
Just schedule your tours about 1.5 hours apart. We purchased tickets online because we thought we could have some trouble getting in on Labor Day weekend. We went on the Monday of Labor Day and it was possible to get in without advance tickets. There was just a 60 minute wait. We could have saved the $2 per ticket “processing fee” if we’d just purchased them on-site.
There is plenty to do while waiting. There is a family room available for sleeping, changing, nursing, rocking, etc. There is also a café (mostly soups, salads, sandwiches and snacks, but made with all-natural ingredients), gift shop and exhibit room. I made use of the trails, exploring the grounds and taking in the views while waiting. Most paths are stroller accessible, so I only had to carry River down on set of stairs and along one hiking trails.
Note that trail H, which is supposed to go to a beautiful view north of the house is NOT worth it in summer. The leaves on the trees block almost the entire view.