Family of 5 16 day trip in Japan

Hi Daniel!
Seeing all the good advice provided already on the forum, could you please advise the worth of the JR pass, ideally 14 days for the following itinerary (travelling 4 full fare 1 child fare):
Oct 26th Arrival Kansai, htl at Shin Osaka w/o JR pass
Oct 27-29 activate 14 day pass to Hakata (day 1-2)
Oct 29-31 Hakata-Hiroshima (incl 1 day trip to Miyajima) (day 3-4)
Oct 31-Nov 5Hiroshima- Kyoto (incl 1 day trip to Nara) (day 5-9) stop at Himeji
Nov 5-10 Kyoto-Tokyo (incl 1 day trip to Fujikawaguchiko) (day 10-14)
Nov 10 depart Haneda w/o JR pass

Thank you