Will this Work?

Hello, we are travelling for 6 weeks in Japan, beginning March 19. Does this itinerary sound feasible and can we use the JR rail pass for the majority of our travels? Also, would we require one 21 day pass and one 14 day pass?

March 19 in Tokyo 5 nights with one side trip to Mito or Kamakura
March 24 to Nikko for 3 nights
March 27 to Hakone for 3 nights
March 30 to Kyoto for 7 nights with days trips to main tourist areas and Osaka
April 7 to Nara for 2 nights
April 9 to Koyo San for 3 nights
April 12 to Hiroshima for 3 nights, with a stop at Himiji and a day trip to Miyajima
April 16 to Kanazwawa for 4 nights
April 20 to Takayama for 3 nights
April 23 to Nagano for 2 nights
April 25 to Tokyo for 3 nights

Thanks in advance, Laura