N'EX TOKYO Round Trip Ticket does not fully cover the fees for the whole route until Kawaguchiko Station.
Currently the route of
Narita Express 8
(starting from Narita Airport Station in Terminal 1)
and Narita Express 41 (heading to the airport)
is extended on Saturdays, Sundays and public holidays until the 26th of November to Kawaguchiko Station of Fujikyuko Railway (, which is also called as Fujikyu).
The JR section Takao -- Otsuki and the Fujikyuko section Otsuki -- Kawaguchiko are outside the usage area, so it seems you have to pay the fees for these sections.
http://www.jreast.co.jp/e/pass/nex_round.html (The two Narita Express trains Nos. 8 and 41 both skip Takao Station.)
Total of estimated one-way additional fees
= 2450 yen per adult.
: 580 yen: JR basic fare for Takao -- Otsuki.
: 330 yen: Gap in JR Limited Express surcharges
between 2350 yen until Takao and 2680 yen until Otsuki.
: 1140 yen: Fujikyuko basic fare for Otsuki -- Kawaguchiko.
: 400 yen: Fujikyuko Express surcharge for Otsuki -- Kawaguchiko.
When you plan to make another long side trip by Day 3, to Nikko for example, JR TOKYO Wide Pass may be suitable.
http://www.jreast.co.jp/e/tokyowidepass/index.html Unlike the N'EX discount ticket, this pass can cover Fujikyuko basic fares Express surcharges.
Like the N'EX discount ticket, only foreign passport holders are eligible for this pass.
For your way back to NRT, it depends on the location of your starting point what transportation modes and passes or discount tickets may be a good choice.