October - Family first trip to Japan

Hello,
We are a family (my husband and I + 4yrs old) traveling to Japan in October and trying to figure out whether we should purchase the 7 days JR Pass.

Here is our itinerary:
10/9: Arrive in Osaka
10/10: Osaka - Universal Studio
10/11: Osaka - a day tour to Kyoto (via bus through agency itinerary)
10/12: Osaka to Tokyo
10/13: Tokyo - a day tour to Mt. Fuji (via bus through agency itinerary)
10/14: Tokyo - Universal Studio
10/15-10/16: Tokyo
10/17: Tokyo to Haneda Airport departing at 3pm

My question is - is it worth for us to buy the JR Pass valid for 7 days and when do we activate it? Shall we activate it on the day we arrive in Osaka (9 Oct)?

Thank you for any advice you can provide!

Best Regards,
Jackie