A recent attempt to answer the question about getting to Kawaguchiko was made in this thread: Tokyo-Kyoto with Hakone and Kawaguchiko / Mt Fuji posts #17 and onwards.

I’ve never been to Kawaguchiko because I’ve never been anywhere specifically to “see” Mt Fuji. I generally assume a 66% chance of not seeing it (greater if I can’t be in an area within two hours of sunrise or at sunset).

As Hakone is the first place I ever spent with my now husband, that’s where I return to, and it’s ideal for trips with the very young and the elderly. So long as there isn’t seismic activity to close off the area, it’s extremely easy and rewarding to explore using a wide variety of transport modes included with the Hakone Free Pass https://www.odakyu.jp/english/passes/hakone/
The Hakone Tozan railway is one of the steepest in the world and employs a switchback system (avoid peak hours if you can as it potentially gets very full in the carriages). There is also a cable car/funicular, spectacular views from the ropeways and the kitschy themed ferry ships for trips across Lake Ashinoko. The Hakone Free Pass is a great way for someone with little legs to cover a lot of ground.
The “woods of net” area in the Hakone Open Air Museum is quite magical for someone your daughter’s age
https://www.hakone-oam.or.jp/en/kidsfamily/