Traveling to Japan with family

Hi,

I am traveling with family (11 year & 14 year kids) to Japan in March end with the following itinerary. Please advise your views :

Day 1 : Reaching to Tokyo at 11 am. Leisure / Rest Day as we will be traveling from Dubai.
Day 2 : Mt. Fuji 5th Station, Ninja Village, Owakudani Valley, Hakone Ropeway, Lake Ashi Cruise, Hakone Shrine. Return to Tokyo.
Day 3 : Explore Tokyo (Tokyo Tower, Ueno Park or Imperial Palace, Shibuya Crossing)
Day 4 : Nikko Toshogu Shrine, Kegon waterfall, walk along Lake Chuzenji
Day 5 : Transfer to Osaka & Leisure Day
Day 6 : Universal Studio
Day 7 : Explore Osaka (Osaka Castle, Shinsekai, etc.)
Day 8 : Day Trip to Hiroshima & return to Osaka.
Day 9 : Day trip to Kyoto & return to Osaka
Day 10 : Day trip to Nara & return to Osaka
Day 11 : Leisure Day or Visit Nagoya (Please advise if it is worth visiting Nagoya with the proposed Itinerary)
Day 12 : Return to Tokyo & Leisure Day
Day 13 : Return to Dubai

Please let me know any suggestions/improvements in the above Itinerary. Also, advise JR pass for the above Itinerary is worth. I have checked on JR pass website, it shows not much benefit as I need to buy 14 days Pass to suit my trip.