I would get in the car in the evening and travel as far as possible while he plays with soft toys, is interested in the trip, or perhaps put a movie in a DVD player then stop and have an evening snack and put on jammies. Then get back in the car and drive for as far as possible until whomever is driving can drive no more.
I would think driving to Chicago and then stopping for the snack would be good. Then perhaps on to somewhere close to Indianapolis for the rest of the night.
I personally liked to drive at night when the traffic was lighter and I could just go, drive and not have anyone else awake to distract me. Since the trip is about 24 hours of just driving I would plan on stopping every 3 hours for either a snack or meal with play time scheduled for each stop.
Stop at a hotel for the rest of the night. I would say the next morning you have some choices to consider while planning out the trail.
Option 1.
You can get up super early and the other adult drive while the child remains asleep and the driver from last night continues to sleep too. Then you can get some more miles on the trip before stopping for a good breakfast. I would dress the toddler at that time and perhaps change drivers back too. I would also choose some place that has a playground so the toddler can run amok and get some of his energy out.
Then after that everyone get back in the car and start on the road again. Schedule would be like this. Breakfast, mid-morning snack, lunch, afternoon snack, dinner, evening snack.
Option 2.
Drive in the evening as far as possible then stop for a late evening snack. Go to a hotel and have some play time by the pool and use the amenities as long as they are open. Go to the room and get a full nights sleep. Everyone wake up in the morning, maybe 7-7:30am and get dressed for the day, everyone awake. Eat breakfast at the hotel as part of the bill.
Travel as much as possible until about 9:30 or 10am then stop and have a snack at a place with a playground where your child can run around and play out all his energy. He will probably go to sleep for a while after getting back in the car too.
In my experience while traveling with smaller children it is good for an adult to be beside them to pick up toys and be able to distract them so the driver can just drive and watch traffic.
The toddler needs to be able to enjoy the trip too.
He also is going to realize once he has been in the carseat for a while that each time it's time to get in the vehicle he is going to fight it like a wild cat. My friend who traveled to Houston to look at houses for a move had to have 3 people hold her toddler down to strap him in. He cried for a little bit but he got over it.
Going on a trip in a car with a small child is fun but trying to the nerves if you don't take your time and allow the child to have some normal things, like playing time. A small child needs that. They can't tell you "Hey, my hiney is getting numb here. I WANT TO GET UP FOR A WHILE!!!!".
They just get whiny and cranky and try to let you know the only way they know how.
I would drive from Green Bay to Chicago, over night stop, then to Indianapolis, stop, then to Louisville for lunch, then on to Nashville for a snack, I might stop somewhere around here for the night but it might be still light. Depends on how the day went. If he can get more travel done then go on and keep moving.
Nashville might be about half way so if you could do the trip with one night in a hotel and 10-12 hours each day that might be the way. I think I would take a more leisurely aspect and stay 2 nights in hotels and make more stops. It would be a much more pleasant trip in my mind. Like Indianapolis, Atlanta then on into Florida.