Your big transportation problem is how to see the alpine route from Kyoto, and then get to Tokyo. going to Amanohashidate will also cost a lot. The first thought is to use a JR Pass.
Amanohashidate is a two hour train ride from Kyoto Station, and that's if you take the limited express train. The first one leaves at 9:30 AM, and arrives at 11:30 AM. The last limited express train departs from Amanohashidate at 6:47 PM, so, it is possible to do this as a side trip, but I would recommend this as an overnight stay, and spend more time there. The JR pass will pay for most of the limited express train, but there is a portion of the tracks that is owned by a private company, so expect to pay a surcharge for this section to the conductor.
That said, two days in Kyoto , which includes a side trip to Amanohashidate is a bit rushed.
You might look into adding Takayama to your trip, and use the Nohi Bus line to get there. You can get to the alpine route from here. The Nohi Bus line has a bus from Kyoto to Takayama, and another one from Takayama to Tokyo. Here is a link to the Nohi bus line:
http://www.nouhibus.co.jp/english/Check out the bottom of the page for the convenience packages for the Alps. I would also think about going to Shirakawa-go from here. This is changing your itinerary around a bit, but this could be very cost effective
So, it is possible, and may cost less, to use the bus. If you do get a JR pass, and you really want to go to Amanihashidate, I would suggest that you cut back on Osaka and Kobe, and include Miyajima and Matsushime, and get all three of the most scenic places in Japan. This is somewhat of the "In for a penny, in for a pound" point of view on the JR Pass.
http://www.japan-guide.com/e/e2250.htmlI hope this helps.
