First visit to japan with Infant and Teenager

Hi.
We have started to look in to a family trip to Japan as a late quinceanera present to our daughter that will be 16 at the time of the trip and our infant will be 8-10 months so will will in total be 2 adults 1 16-yo and a almost 1-yo.
We have been thinking about starting our trip in Tokyo most likely landing at Haneda and spend a few days in Tokyo with the obvious visit to Disneyland for the teenager and some shopping.
And then we have been thinking about a few nights stay in either Osaka or Kyoto and doing daily Excursions to cover Hiroshima, Kyoto, Osaka, Lake Biwa and what else we manage spending some where around 5-7 days in te region.
But there is 2 things we have been trying and failed to find a good answer to and that is.
1. How is it to travel on the Shinkanse with a baby stroller and luggage?
2. What would be the most cost efficient way of doing this trip i have tried to put it together in the Fare Calculator but not managed Should we look in to the 14 day National ticket or maybe 2 different regional tickets? or a 7 day national and then regional or subway for the time spent in Tokyo?

And a bonus question we are discussing the timing of the trip and as it looks now it will either be mid June and roughly 14 days or end of July/beginning of August and roughly 14 days is there any time that is better than the other?