I'm not entirely clear on what you're expecting to get out of Kamakura? It's "Tokyo's Kyoto" and a worthwhile day trip for the time-constrained Tokyo visitor, but since I gather your rather audacious itinerary is already taking you through the length and breadth of Japan including plenty of time at the actual Kyoto, it hardly seems necessary to cram in yet another temple town.

Yes, there's a big Buddha statue, but there's one in Nara as well, and Hasedera and Hachimangu are (shh) a rather forgettable temple and shrine respectively. There are a couple of cozy neighbourhood temples for a cup of tea in the garden and that sort of thing, but again, you can find these in any Japanese city.

To be clear here, I actually like Kamakura. But if you're staying in Hakone for two nights, then stay in Hakone for your one single whole day, instead of bouncing around like a billiard ball.