Hi there,
Unfortunately, the Fuji Hakone Pass which includes the expressway bus ticket from/to Shinjuku is valid for only 3 day from the date of first use. So, the Fuji Hakone Pass might not be the right choice for you.
If you want to go to Kawaguchiko and spend a few days in Mt. Fuji area, I would recommend that you just purchase a round trip ticket from Shnjuku to Kawaguchiko from the following website.
http://highway-buses.jp/fuji/
Then, you can just take local buses which connect major sightseeing spots. No reservation is needed for those local buses.
Please see the link below for more information.
http://bus-en.fujikyu.co.jp/
Other option is to use Q-pack tickets.
The Q pack ticket includes a round trip ticket from Shinjuku to Fujikyu Highland and a one day free pass for the Fuji Q Highland which is one of the most thrilling amusement park in Japan. As your children are over 12 years old, Fuji Q highland may be a fun place to enjoy all day long. There are also Fujiyama onsen (hot spring) in the same place, so you can enjoy hot springs as well.
http://www.fujiyamaonsen.jp/index.html
You can take a local bus from Fujikyu Highland to Kawaguchiko.
As for the luggage, you can bring your luggage into the highway buses. Also, once you arrive at Kawaguchiko, there are a lot of lockers and places where you can leave your luggage.
http://fuji-bb.jp/welcome/
I hope this information help you.
Have a nice trip!
Let us know about your trip!
