5 days in Tokyo and Hakone

Hi, my family (2A & 2C 7&10yrs) arrv Narita pm. and will stay 1 night in Narita & have a look around Narita town next day for a few hours. We then go to Asakusa. Accom. is booked for 2 nights, sights of Tokyo - my next post, then we want to go to Hakone for overnight trip. Here is where my questions start ... has anyone stayed in Japanese style with private bathroom with children? Where is best to stay when doing the Hakone round course. In our short stay we would love to catch the Shinkansen, is this possible on our Hakone trip or is there somewhere else we could go for this experience? I was going to book with a private organised tour, what are your thoughts? Thank you so much.

For an overnight trip to Hakone from Tokyo,
(1) the economical choice would be to buy the Hakone Free Pass that includes the Odakyu train ride from/to Hakone area from Shinjuku and all the cablecars, etc. within Hakone.
(2) If you definitely want Shinkansen ride, then you can take the Tokaido Shinkansen from Tokyo to Odawara, then from there just buy the "within Hakone" version of the Hakone Free Pass, which is less expensive compared to the one from Shinjuku. But the Shinkansen ride will cost you some.

For accommodation, rooms with private bath can be expensive, so maybe you can stay at a place with "kashikiri buro" (rent-to-yourself bath) or "kazoku buro" (family bath) that the family can use by youself for 40 minutes or 1 hour (depends on the place). What kind of budget do you have in mind?

Many thanks for your advice and time, it was very helpful, I appreciate it. Cheers.