You should note that late November is the autumn foliage season in Kyoto so the accommodation tend to be busy and expensive.
https://goo.gl/xwp7cdThis is the result of Booking.com and you will see many hotels accommodating two adults and two children are around 1500 USD for three nights. You can find cheaper hotels but they usually provides very small rooms.
As you see, Kyoto Hanafuji Annex is rather inexpensive (743 USD for three nights) and provides very large room. Actually this is a whole house (probably for a local family) and may be recently opened so this is still available.
https://goo.gl/s95HCuThis is not in the touristic place and you must do some train rides, but the price and the space is exceptional. This can be cancelled for free so I would recommend you to book it soon.
Or this might be better.
https://goo.gl/tfWQqTCheaper, more centrally located, but less space (still spacious I think).
As for transportation, Takayama Hokuriku Area Tourist Pass can be used for your transport from KIX then Kyoto, Kanazawa, (bus) Shirakawago, Takayama and Nagoya. You must pay additionally from Nagoya to Osaka though.
https://www.japan-guide.com/e/e2361_takayama_hokuriku.htmlThis pass is valid for 5 days so if you do your itinerary, it will be expired at day 5. So you might better use it from Kyoto. To get to Kyoto, Icoca & Haruka would be useful.
https://www.japan-guide.com/e/e2359_icoca_haruka.htmlFrom Nagoya to Osaka, you might better consider taking Kintetsu train (Limited Express) which is cheaper than Shinkansen although slower.
The revised itinerary is:
26/11- Reach Kansai Airport @6am
-Kyoto
27/11- Kyoto (Arashiyama)
28/11- Kyoto (start of the pass though you might have no chance to use it for the first day)
29/11- Kanazawa
30/11- Shirakawa-go (stay Takayama)
1/12- Takayama
2/12- Nagoya (end of the pass)
3/12- Nara, Osaka (by Kintetsu)
4/12- Osaka
5/12- Osaka
6/12 - 10:30am flight @Kansai airport
I think you can wash your clothes so 3 days of clothes for your family would suffice. Big luggage is troublesome especially in your first Kyoto day and 5th Shirakawa-go day. You don't need to bring towels or toiletries so I believe one "carry-on" size backpack for each person would be enough.