[Transportation passes]
A Kansai Thru Pass is a non-JR transportation pass, which cannot be used on the JR section Osaka -- Kyoto on Tokaido Line.
This JR section is usually called "JR Kyoto Line" by JR-West in its announcements and signs.
Whether a transportation pass pays off or not depends on places to visit, but now I do not think of any intercity transportation pass which may save much cost in this journey.
Will you fly into and fly out from Kansai Airport [KIX]?
Which places will you visit in Osaka and in Kyoto?
How old will the two kids be?
You can travel between Osaka Station (in Umeda [Kita] area) or Shin-Osaka Station and Kyoto Station at 560 yen per adult per way using JR Kyoto Line.
You can travel between Umeda Station (of Hankyu) / Shin-Osaka Station (of subway) and Karasuma Station (of Hankyu, in Kyoto City) at 400 yen / 580 yen per adult per way using non-JR lines.
A one-day Enjoy Eco Card, which can be used on Osaka Municipal Subway, New Tram and Bus lines, is available at 800 yen per adult for a weekday or at 600 yen per adult for a Saturday, a Sunday or a holiday. (The child edition is available at 300 yen regardless of dates.)
A Kyoto City Bus - Kyoto Bus One-day Pass, which can be used for bus accesses to and from many major tourist spots in Kyoto City, is available at 500 yen per adult. (The child edition is available at 250 yen.)
[Possible crowdedness and the order of places]
The weekend from Saturday, 22 November 2014 will be practically expanded to be 3 days, because Sunday, 23 November will be a national holiday and 24 November will be a substitute holiday.
That may have caused your difficulty in finding good accommodation in Kyoto City from 23 to 25 November 2014.
Major tourist spots may be crowded with visitors during this expanded weekend, especially some in Kyoto City if they are still in the autumn foliage season.
If you come in the morning of Friday, 21 November, it may be better to travel in Kyoto City earlier, visiting some most popular spots by around the noon of Saturday, 22 November.
[Accommodation and transportation]
In terms of convenience of transportation,
Umeda [Kita] area and Shin-Osaka area in Osaka City
and Kyoto Station area and Shijo-Karasuma area in Kyoto City
sound nice for your accommodation.
Osaka Station in Umeda area, Shin-Osaka Station (of JR-West) and Kyoto Station (of JR-West) are on JR Kyoto Line and connected by JR direct trains.
A one-way JR ride in a Special Rapid train between Osaka or Shin-Osaka and Kyoto lasts for about 25 to 30 minutes. The one-way fare is 560 yen per adult.
A large bus terminal is on the Karasuma side [north side] of JR Kyoto Station near Central Gate.
Hankyu trains connect Umeda Station in Osaka City and Karasuma Station in Shijo-Karasuma area of Kyoto City.
A one-way Hankyu ride in a Ltd. Express train lasts for about 40 minutes. The one-way fare is 400 yen per adult.
Shijo-Karasuma area in Kyoto City is around Shijo-Karasuma crossroad of east-west Shijo-dori and north-south Karasuma-dori, which is about 2 kilometers roughly to the north of Central Gate of JR Kyoto Station.
In this area, Hankyu has Karasuma Station, Kyoto City Subway has Shijo Station and a bus terminal is on the basement of subway Shijo Station.
Osaka Municipal Subway has Umeda and Shin-Osaka Stations, which are connected by direct trains on Midosuji Line in about 5 minutes. The one-way fare is 240 yen per adult.
In Umeda area, JR-West has Osaka Station, Hankyu and Hanshin have Umeda Stations and Osaka Municipal subway has three stations including Umeda Station.
Depending on places to visit in Osaka City, Umeda area is better than Shin-Osaka area to start from and/or return to.
(e.g. You can travel by Hankyu from Umeda Station to Mino-o Station, which is a gateway to Mino Park in Minoh City known for a scenic fall. It is a long way of about 3 kilometers to walk from the station to the fall, though.)
[Travelling from KIX to Osaka City or Kyoto City]
If you travel from KIX to Osaka City, please note
that Rapid trains for Osaka do not run to Shin-Osaka Station
while Airport Ltd. Express "Haruka" trains for Shin-Osaka and Kyoto do not make a stop at Osaka Station.
When you take a JR "Haruka" train first but head to Umeda area, you can change trains in Tennoji Station(s) in Osaka City
either to a JR train for Osaka on Osaka Loop Line inside JR gates
or to a subway train for Umeda on Midosuji Line via a JR exit gate and a subway entrance gate.
A foreign traveler with Temporary Visitor status of residence can choose a one-day or a roundtrip JR-West ICOCA & Haruka package.
(If one or the both of the kids have not reached 12 by the boarding date, a possible demerit will be that a child-rate edition is not available concerning this ICOCA & Haruka package. In that case you may prefer taking a Rapid train with regular tickets to save the cost.)
http://www.japan-guide.com/e/e2359_icoca_haruka.htmlA ticket in this package can pay off if you take a JR "Haruka" train between Kansai-airport Station and Tennoji or Shin-Osaka or Kyoto Station, partly or fully on the way between KIX and Osaka City or Kyoto City. Please note that this ticket is a one-way one-day ticket, not a rail pass.