Tokyo-Kyoto-Hakone-Tokyo

Hello

We're a family of four including two young children 6 and 9 travelling to Japan in December for 10 days.

Am planning my itinerary now and would appreciate your advice in terms of easy of travelling/transportation.

Question:
1) Is it better to travel from Tokyo (Haneda) to Kyoto then to Hakone and back to Tokyo (Narita) or Tokyo-Hakone-Kyoto-Tokyo?

2) Does a JR Pass connects us on the Shinkansen from Tokyo to Kyoto/Hakone and back to Tokyo?

3) Do I have to buy a separate local pass like the Hakone Free Pass for Kyoto or does the JR Pass include local buses and trains in Kyoto.

Looking forward to your advice.

1- Doesn't matter which way you do it. The transfer station (Odawara) is the same.

2- Yes.

3- The JR pass only covers JR trains and buses in Kyoto.