Chgogal, thank you for your suggestions. I have booked the Asakusa Tobu hotel. I have 2 hotels booked in Tokyo which I do not like to do, but once I work out our itinerary I will cancel one.

It's possible to visit both Odawara Castle and Kamakura on the same day! We did it, and it was not really hard.
1. Odakyu Shinjuku Station -> Odawara Station
2. Odawara Station -> Ofuna Station -> Kamakura Station

Yes, easy to visit both, particularly if the only think you want to do in Kamakura is see the Daibutsu. But there is MUCH more to Kamakura than just that one temple, and if you consider the delights of Kita Kamakura, too, some people would want more than a day in Kamakura. It depends on what one wants to see and experience.