Yeah, it doesn't really matter, greatly, which way you do them. With your itinerary start in Tokyo and then go to Kyoto and Osaka. Especially with young kids who probably won't enjoy too many long travel days.

How you split them, as said above, depends on your interests. I'd say spend most of your time in Tokyo and Kyoto and less in Osaka as the first two have lots more to do. You really need to get a good guide book or look on Japan guide to see what's available. For daytrips you could try Nara or Himeji.

For luggage you can use Yamato which has a next day delivery service across Japan. It's very reasonable and (I'm pretty sure) all hotels will arrange the service at reception/ the concierge.
http://www.kuronekoyamato.co.jp/en/tourist/hotel/