Or should I buy another pass to go along with it?Honestly, your itinerary give train fans (like me :) a very interesting puzzle, and the answer is no, as shown below.
3/31 Kobe - Mt Koya (only taking overnight bag): Spend night at KoyaYou need to take Nankai line to Koyasan. JR pass or Seishun 18 Kippu does not cover travel to Koyasan.
http://goo.gl/kGoNhU4/1 Koya - Kyoto or Osaka - Kobe: Return to Rokko Island.You can see most of Koyasan during your first day (3/31) in Koyasan. Then you may be able to start in the morning to Namba. I think you should do Osaka sightseeing on 4/1 and assign 4/2 and 4/3 for Kyoto.
I recommend you to buy Kansai Thru Pass 3 days (5200 yen for adults and 2600 yen for children). You will be able to use the pass for 3/31 and 4/1, and the rest one day for 4/4.
http://www.surutto.com/tickets/kansai_thru_english.htmlBuy Autumn/Winter version somewhere (Osaka Umeda, Shin-Osaka etc.), maybe on 3/28 when transfering shinkansen at Shin-Osaka, or on 3/30 you can go to Shin-Osaka, buy Kansai Thru Pass there and get a JR to Sumiyoshi and then Rokkoliner to Island Center.
To and from Namba(Nankai)/Koyasan, you may want to take limited express which requires reservation and the seat fee. The limited express is more comfortable so I reccommend to take it, considering you have little children with you. In that case you must pay additional 780 yen per person, one way.
If you want to buy reserved seat ticket, you should start early.
http://goo.gl/Lm8Fqzhttp://goo.gl/UMzL2zLimited express ticked for Koyasan is sold at Namba (Nankai) station. I think you can buy it on the day. You can also buy Kintetsu reserved seat ticket for 4/4, at Hanshin/Kintetsu Osaka-Namba station. Your train reaches at Osaka-Namba, so you should buy tickets for 4/4 first, and then walk to Namba(Nankai), and then buy tickets to/from Koyasan.
4/4 Kobe - Iga - Kansai Airport: Ninja festival. (Note, hope to check bags at a station en route to Iga, that we can pass back through on return to Kansai and pick back up). Stay at Kansai airport hotel:Use the rest Kansai Thru pass.
To Iga (Uenoshi):
http://goo.gl/XFnXtGIn this case also, you may want to take limited express (900 yen/person). As described above, you should buy it beforehand, on 3/31.
The pass covers from Island Center to Igakambe, but you must pay for Igakambe to Uenoshi (360 yen/person, and 180 yen for your 8 yo child).
You should drop your luggage at somewhere on the way, maybe at Osaka-namba, then you should start early.
http://goo.gl/VQ6WL7and then
http://goo.gl/cVqtMsFrom Iga (Uenoshi): to Osaka-namba:
http://goo.gl/sa75tVPick-up your luggage and then walk 12 min to Namba(Nankai). There should be many signage in English.
Namba(Nankai) to Kansai airport.
http://goo.gl/1bQ2fuAs you see, there is not so much difference in time to reach the airport between using limited express (510 yen/person).
The Seishun 18 will be available during our trip, would that make sense for any portions?I don't think so, since Seishun 18 is only valid for JR trains which do not cover Koyasan. Further it is a set of 5 tickets (there is no child fare) so that you can not use them efficiently.