I dunno....if I were in your position and I wanted to visit Kamakura, I'd definitely go. I'd sent everything to the airport by takkubin except for the necessary items in kamakura, which in my case, would be zero, maybe a sunscreen bottle. I would take Tokaido line to Fujisawa from Odawara (less than 1 hr from Odaware) and jump on the Enoshima line, to one of the stations near Kamakura, walk by the shrines to Kamakura, and if on a weekend, jump on a NEX from there, or if not, take a Yokosuka line to Ofuna and jump on a NEX there. I think its definitely doable and not that out of your way. I would NOT drive at ANY COST and I would not take car service except maybe to Odawara station.