JR Pass advice

JR,

Myself and my family (wife and three daughters aged 10, 6 and 9 months) will visit japan in February for 14 days. The plan is to arrive in Narita Airport and get the train to our hotel in Tokyo. Then spend 4 nights in Tokyo, travel to Kyoto for 4 nights and then to Karuizawa for 5 nights and ski. We then travel to Narita airport from Karuizawa on the 14th day.

I have used the itinerary planner on this website and it looks like the round trip comes in about 3900 yen less than the price of a 14 day pass (for an adult).

Obviously we will probably travel a lot in Tokyo and Kyoto but wont need the pass for 4 days whilst skiing. I know you cant use the JR pass on the subways so my question is:

Is it better to get the tickets from Narita - Tokyo - Kyoto - Karuizawa - Narita separately and then get tickets as required as we travel around Tokyo and Kyoto or are we likely to use the JR pass more and save money?

(We plan to do Mt Fuji from Tokyo and probably travel to Osaka from Kyoto if this helps?)

Can you also please confirm my 9 month old baby travels for free?

Thank you for any advice!!!