Family of 5 traveling to multiple cities

Hello! We are a family of 5, 2 adults and 3 children (11, 7 and 5 years old).
June 28th arrival at Narita intl airport and travel to Tokyo Bay Hilton. (Will explore Tokyo on June 29, dismay sea on June 30)
July 1 we travel from Tokyo to Hiroshima, stay for 2 nights
July 3 we travel from Hiroshima to Osaka (will do a day trip to Kyoto)
July 5 we travel from Osaka to Narita (possible day trip to Tokyo)
July 7 depart out of Narita

We were looking at the Shinkansen for all of our travel but it’s quite expensive. Wondering what the best option would be? And how do I get a ticket/seat for our 5 year old - there is no purchase option for under 6.

Thank you
Karyn