Tokyo to Kawaguchiko to Magome

My wife and I will be traveling to Japan with our 4 month old daughter. After spending time in Tokyo, we want to see Kawaguchiko before continuing on to Magome to do the hike to Tsumago. We will have a JR pass. A few questions:

1. Is there enough time to leave Tokyo in the morning, see Kawaguchiko sufficiently, and then get to Magome all in one day? Or should we sleep in Kawaguchiko?

2. To get from Kawaguchiko to Magome, is it better to go back to Tokyo and take the Shinkansen to Nagoya rather than the other JR train through Shiojiri? If this is the case, would it be better to handle Kawaguchiko as a day trip while we are still based in Tokyo?

Kawaguchiko
You could easily spend a whole day visiting the area.

Magome to do the hike to Tsumago

If you are planning to do the hike the same day after visiting Kawaguchiko, IMO, you'd be "rushing". It will take at least 3 hours for the hike, not to mention the journey to either Magome or Tsumago.
I did the hike a few years ago, attracted by the ad picture on this website; honestly, could be a wrong time of the year? but "the hike" was the most boring and time wasting experience of my many hikes in Japan.

No need to stay at Kawaguchiko.

Also not need to take a Shinkansen to Nagoya, waste.
Go out to Matsumoto and go to Magome by LtdExp Shinano of JR.
https://goo.gl/maps/YRE94Hj8nMt
(FujiQ railway section is not covered by JRP.)

To get from Kawaguchiko to Magome
Just bear in mind that the journey would take about 5 hours, or more depending what train you are taking.

Overall, I agree with the above comments, although there was the following:

Go out to Matsumoto and go to Magome by LtdExp Shinano of JR.

You COULD do that, but you could also get off at Shiojiri Station (one stop before Matsumoto on the Azusa Express) and transfer there to the Shinano Express train going south. The connection time might be better at Shiojiri. Even if it's not, you'd spend about 10 minutes less time sitting on each of the two trains.