Kawaguchko-Hakone-Kamakura itinerary

Hi, we are planning to visit Tokyo and surroundings end of Nov this year. So far I have 5 nights Tokyo and 3 nights Kawaguchiko ( I love mountain areas). After that, Im thinking to go Hakone for 2 nights and then Kamakura for another 2 nights before heading back to Tokyo for another 2 nights.
Or should we go Kamakura first and then Hakone? We have decided t rent a car. Which is nearer to Tokyo? Kamakura or Hakone? Where is the nearest station to take the shinkansen back to Tokyo from either Kamakura or Hakone depending on which we go first?
Appreciate any advice you can give. Thanks in advance.

Your statements are confusing: are you driving or taking the train???

Open the Google map - Kamakura is closer to Tokyo than Hakone.

On the map, Kawaguchiko and Hakone look close together, but there is no direct train service between them. So, it is better to drive or take a bus.

Kamakura is so close to Tokyo, there is no need to ride Shinkansen.

The nearest Shinkansen station to Hakone is Odawara.

You dont need Shinkansen either from Hakone no from Kamakura. Its pretty close both . Shinkansen are pretty expensive from Odawara. Take rapid Trains