Chubu ininterary & rail pass info

Hello everyone. I'm traveling to Japan with my family in late October/early November. I lived in Tokyo for a year in 2003 so I can speak Japanese and know my way around quite a bit. However, this is my first time really ''vacationing'' so I need some advice. So far our itinerary is as follows:

10/21-10/25: TOKYO
10/25-10/28: KYOTO with possible day trip to NARA
10/28-10/30: KOYA-SAN
10/30-10/31: OSAKA

At this point my mother and sister return to Narita and fly home, leaving my father and I free until we leave on the evening of November 4. My dad and I would like to do something in the Chubu region and we are particularly interested in Takayama and Shirakawago.

We've discussed potentially traveling through Kanazawa and Toyama to create a loop, but given that we have really only got three days that seems like it might not be enough time to see anything. Here are my questions:

1) What is the best route from Osaka through Takayama/Shirakawago and back to Tokyo? Out and back through Nagoya?

2) I've looked at the possibility of returning to Tokyo through Matsumoto to Nagano, but it seems like that takes quite a bit of time due to the bus/train trip from Takayama to Matsumoto.

3) We are considering renting a car in Osaka and returning it in Nagoya or Nagano to return to Tokyo via shinkansen. Do you think this is a worthwhile venture? Will it enable us more flexibility to see the countryside? Will it save us money? Will it be faster than taking the train and busses?

4) On the subject of finances, I would like your opinion on the value of purchasing a 2-week Japan Rail pass (currently about $400). Osaka/Takayama/etc. seem to be JR. It seems like getting the pass will be well worth it if we make this trip by train, but what about if we rent a car? Most of the lines between

Thank you all for any input you have. I've been puzzling about this for a while and I can't seem to come up with the best conclusion. Arigatou!

What is the best route from Osaka through Takayama/Shirakawago and back to Tokyo?

I recommend:

Osaka - (train) - Kanazawa - (bus) - Shirakawago - (bus) - Takayama - (train) - Tokyo

For example in more detail:

Nov 1:
leave Osaka for Kanazawa in the morning (2.5 hour train ride), see some sights in Kanazawa until catching the 14:40 bus from Kanazawa to Shirakawago, arriving in Shirakawago at 15:55 (there are only two buses per day from Kanazawa to Shirakawago); spend the night in Shirakawago

Nov 2:
see Shirakawago and take the bus to Takayama in the afternoon (2 hour)

Nov 3:
see Takayama

Nov 4:
return to Tokyo via Nagoya (5 hours)

I've looked at the possibility of returning to Tokyo through Matsumoto to Nagano, but it seems like that takes quite a bit of time due to the bus/train trip from Takayama to Matsumoto.

It would be about one hour slower than going via Nagoya, but the bus between Takayama and Matsumoto is not covered by the Japan Rail Pass.

We are considering renting a car in Osaka and returning it in Nagoya or Nagano to return to Tokyo via shinkansen. Do you think this is a worthwhile venture? Will it enable us more flexibility to see the countryside?

Shirakawago and Takayama can easily be explored without rental car. A rental car would not be a great advantage in terms of flexibility.

Will it save us money?

I would have to make a detailed calculation. But just from the feeling, I think a rental car would come more expensive than a rail pass, considering daily rental fee, expressway tolls, gasoline and a drop off charge.

Will it be faster than taking the train and busses?

It can be faster, because you don't lose time transfering between trains and buses.

On the subject of finances, I would like your opinion on the value of purchasing a 2-week Japan Rail pass (currently about $400).

If you only visit Tokyo, Kyoto, Osaka, Shirakawago, Takayama and Koyasan, a 14-day pass will probably cost about the same as (maybe a little bit more than) regular tickets. The buses in the Shirakawago/Takayama region and access to Koyasan is not covered by the Japan Rail Pass.