Another option---Look into taking the Amtrack train from Chicago to East Lansing, than renting a car and driving to Mt. Pleasant (about 1 hour drive). They have one direct train from downtown Chicago to East Lansing (Blue Water 364), leaves Chicago 4:10 pm, arrives E. Lansing 9:29 pm, depending on how far you book in advance, day traveling I saw 1 way ticket as low as $22 (Sept 26), other dates were under $50 each. They also have 2 other trains that you can take, but you will get off train in Battle Creek, and than they put you on a bus that will take you to the East Lansing Train station. Those times were may actually be better for you.
The key is to book early---as the train fills up, prices go up. Also, check "hot deals" sometimes you can find a fare actually cheaper there than on the regular website. But those are kinda of a hit or miss. My daughter took the train last fall (had to take bus from East Lansing, to Battle Creek, than train) had direct train back. No problem--other than train was late coming in to Chicago---they share tracks with freight so trains can be delayed.
Anyways, this may be a less costly way, you will have to get a hold of Amtrack to find out how to get a rental car in East Lansing.
Renting a car in Chicago can be costly (son lives there) tax's are very high. And driving out of the city can be a real pain.