Some important things about your itinerary are still unknown.
Which airport(s) will you use? (It is related to #2.)
When in December 2012? (It may affect where and when to visit popular spots.)
Generally speaking, popular theme parks may get crowded in late December.
As to #3:
If one or some of the four children are old enough, consider staying overnight in Nikko and letting them visit historical / natural assets such as Toshogu Shrine and Kegon fall.
(I hope they can feel Japan. Children can enjoy theme parks in another country.)
From which place will you take a bus? Long-distance buses may get delayed.
Note that Edo Wonderland will be closed on Wednesdays and from 8 through 21 in December 2012.
A Kinugawa Theme Park Pass of Tobu including admission to Nikko Edomura [Edo Wonderland] sounds good for your Kinugawa trip.
: The sum of Tobu regular roundtrip fares and an admission fee of Edo Wonderland is 6000 yen (for an adult).
: One thing to note is that with this pass, you will have to start and end your trip at Asakusa Station of Tobu.
: Paying 1300 yen per way (for an adult) as a charge, you can take a direct Ltd. Express Kinu, which may be a good choice if you seats for all the travelers are reserved.
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http://www.japan-guide.com/e/e2358_002.htmlAs to #1 and #2:
You cannot take a Shinkansen Nozomi train with a Japan Rail Pass.
If you make a roundtrip from Tokyo to Osaka within 7 days, a 7-day Japan Rail Pass can be a good deal.
: Many Hikari trains are available between Tokyo / Shinagawa / Shin-Yokohama and Shin-Osaka.
: You can use JR-East between Shin-Yokohama / Yokohama and Shin-Sugita.
: A Japan Rail Pass is not valid on the non-JR section between Shin-Sugita and Hakkeijima.
As to #1:
No direct trains are available between Shin-Osaka and Universal-City. A simple transfer in Osaka Station is needed.
It sounds better to stay overnight around Osaka Station.
As to #2:
You had better avoid setting two Tokyo Disney and another theme parks in a short term. Children may get exhausted.
I suggest you ask each of the children to choose one among Disneyland and Disney Sea.
And, I recommend you stay for the previous night in one of Official Hotels for the benefit of guaranteed admission to a Tokyo Disney park.
(Even with this benefit, guests may have to wait long inside the park for some attractions.)
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http://www.tokyodisneyresort.co.jp/en/about/rh/official.htmlAs to #4 and #5:
Yes. The 24th of December 2012 will be a substitute holiday.
In areas where schoolchildren's winter vacation officially begins on the 25th December, practically it will begin around noon on the 21st or the 22nd this year.
In Japan, many people celebrate Christmas in a non-religious way.
(I guess most "Christmas" events are ended by Christmas Eve in Japan.)
Some illumination events are continued even after 25th Decmber, until the end of the year or of the New Year season.