I googled how long it will be to get from Chicago to Disney, and Chatanooga, TN is about the halfway point. If I were you, I would stop no sooner than Chatanooga, and if you can make it, get to Atlanta (which would leave you only about 4 hours until you would get to Disney). Both places should have plenty of cheap hotels and things to do if you are looking to spend some time there.
As for fireworks, Magic Kingdom will obviously have the best, but they will also have the largest crowds. Epcot has beautiful fireworks that go off nightly and I can guarantee that the crowds will be a third of what the Magic Kingdom's are. You are just going to have to figure out what's more important to you.
Stress free driving...no way! However, there are things I suggest to make the driving more bareable. First, if you don't have portable DVD players, invest in them now (one for each). This way, there is no fighting on what movie to watch, and they can be entertained for hours. I also suggest bringing along coloring books, toys, portable gaming systems (we LOVE our Leapster), and maybe a few new cheap toys that you pick up (the "newness" will keep them entertained forever).
If you have not done so already, order the free Disney DVD that will explain more about the parks. It is completely free (there are no catches), and it really does give you a lot of good information. Second, as the time grows closer, begin to plan your days out ahead of time. If you are staying on property, make sure that you participate in extra magic hours (they save you SO much time). I also suggest trying to stay on property. Most of the local hotels are not any cheaper than Disney themselves, Disney offers better perks, and it will make the experience much better for you and your kiddos!
Good luck and have fun! :)
P.S. Just read the last mom's review...Discovery Island no longer exists at Disney World. Don't try and find it, because you would have a difficult time ;)