From Kawaguchico to Nara by car : a stop?

HI,
weere spending 14 days in Japan end of next April, with our 2 daughters (10and 13).
We have our trip nearly all planned except the day we have to travel from Fujikawaguchico to Nara.

D1 - D 4 : Tokyo (wefve already spent 4 days w/o our children some years ago already)
D5 - D9 : Fujikawa (not compressible 4 days cause dad is running the Mont Fuji trail !:-) with the children wefll be visiting around
D10 - D11 – leaving from Fujikawa for Nara : here I need your help
D11 : arrival in before noon to Nara, staying for a night
D12 - D13 : Kyoto
D 14 : Osaka
D15 leaving in the moning


My question: it takes 6h to drive from Fujikawa to reach Nara, but we thought we can make the trip in 2 times and stay somewhere in between for a night. Take time to discover a different face of Japan (tradition, nature, experience an onsen/ festival) compared to what we could have seen in the rest of our planning.

First, we thought going through the Japanese alps and stop by Shirakawaga go or Mathusmato / Shirahone Hot spring, but It is far too gdenseh for just a day, and makes it a long way to Nara (do you agree ?). Also, we consider we have already stayed 4 days in the region of 5 lakes it my be similarc
Second option is to take the south highway throug Shikouza, and try tea picking or stop at Nagoya ? The idea is to sleep overnight the closest to Nara.
Any special tip for a place to stop by, a guest house, Ryokan, onsen tip to visit on our way?
thanks,
May

Why are you driving? - expensive and slow. One-way drop-off fees plus tolls add up. Pretty much every where you mentioned is accessible by fast and or comfortable train (Nagoya is on the shinkansen network afterall). I consider driving a waste of a day when you could be doing something else, but that is your choice.