The trick to getting the most out of the Rail Pass is to plan it so it covers the longest travel days. Since your 14-day Rail Pass will not cover your entire stay, you need to maximize the days it will cover. If you will be in Tokyo for the first 4 or more days, then I'd activate the Pass to cover the last 14 days. If you will be leaving Tokyo immediately and then staying back at Tokyo the last few days of your stay, you should reverse that and have it cover the first 14 days. Either way, you should probably get pre-paid Suica cards for use in and around Tokyo - it is valid on subways and trains - and use the Pass for the longer distance travel.
In any case, you are unlikely to be able to activate your Rail Passes after arriving so late. It will be a rather expensive taxi ride with the late-night surcharge but with a 4-1/2 year-old I'd pay it. You can activate the Rail Pass at any major JR station after you are in Japan.
I'd think your child could ride in the lap for shorter trips but really should have a seat for the longer ones. Shinkansen travel is very comfortable and convenient but only when you are in a seat.