I have "heard" of an outfit called--www.megabus.com
check out the site...
Chicago to Milwaukee at all different times -- $ 1 to 3 a seat one way..
Might do a new thread about megabus to see if any Fodorites have used it..
good Luck

So, here's my total re-working of your plan, which, of course, you can totally ignore.

Leave the kids home with the grandparents. As a grandparent, I'd much rather care for two kids that age in my home (or theirs) than in a hotel.

Stay the night of the concert at a hotel near Rosemont--some have shuttles.

Take the train or bus to Milwaukee and spend the night of the baseball game at the Ambassador Hotel. The owner recently spent $13 million to bring it back to its 1927 glory, and it's beautiful. They have a shuttle to/from Miller Park and downtown

Here is another way to do it. I'd forgotten about the Megabus! Thanks Traveler24. There was an article about it in our paper. Basically it is express bus service. No stops. So here you go:

Drive to St. Louis.
Take the Megabus to Chicago.
http://www.megabus.com/us/
Leave the kids with the grandparents in Chicago.
Take the Megabus to Milwaukee.
The remodeled Ambassador sounds lovely!
And then do the reverse.

As for a place to stay by Union Station, there are loft condos on every block. Try renting one from this site:

http://www.vrbo.com/vacation-rentals/usa/illinois#3122