Travelling family in April

We’re travelling 14 nights in April 21-5 May.
5 nights Tokyo, 2 nights Hakone, 4nights Kyoto (day trip to Hiroshima,) 2 in Osaka, Last night in Tokyo.

Should I buy a JR pass and activate it when travelling from Tokyo to Hakone and buy some single fares end of trip as 7 days pass won’t cover all or should I activate it in Hakone which will cover the rest of travel and buy a single ticket to Hakone as I heard there are a few ways to get to Hakone . by romance car and what is that exactly ? Does it cover the Hakone roam pass too or should I get bullet train to Hakone?
First time in Japan by myself with 3 kids so want to get it right and make super easy for us.

Also is first class pass worth it?
Thanks