Japan in May

Hi!

We are travelling to Japan in May and it looks like the JR pass would work, however, could you please help me confirm this is correct as I am not sure how to calculate the 7 days from activation.

Here is our itinerary:
May 18th - Arrival at Narita @ Noon. Travel to Tokyo Station.
May 20th - Tokyo to Shinagawa
May 21st - Shinagawa to Disneyland - return
May 23rd - Shinagawa to Osaka
May 24th - Osaka to Kyoto - return
May 25th - Osaka to Shinagawa
May 26th - Shinagawa to Haneda

Would the pass work on all stations? When would you recommend me to activate it? Also, I am travelling with a one year old. Do I need to buy a pass for her?

Thank you very much.
Andrea