Hello and welcome to the RTA forums !

A journey of this lenght will take 6 days of driving when allowing for short breaks from the car to stretch the legs, eat, fill with gas, while also tending to the needs of a baby.[and dog]

I can't think of a good reason why travelling at night would be a good idea at all to be honest. It will be disruptive to your sleep patterns, and while spending a good deal of your time in the car for the trip, will miss all the scenery along the way. I would try and keep things as normal as possible and have the day to travel and visit and the night to rest and sleep.

As for the natural wonders I would suggest you do a little research and see what appeals to you and when you have dots on the map, select a route that is most suited to that list. You won't have a whole bunch of time to zig-zag around the country so the attractions and route should start to come together as one, so that it suits your tastes. There is no real time difference to heading from I15 to I70 or taking I40/144, or I10 to I40 and of course you can get off Interstate and use combinations of routes to get where you want.