Yes, Chicago is going to be a major headache on your way to Irving Park, but it won't be your only one. There's also Indianapolis to worry about. My suggestion would be to pull up at the end of your first day of driving in Richmond IN, about 70 miles east of Indianapolis. That would make for a drive of around 530 miles on the first day. That should be quite doable and let you get a good night's sleep before starting out the next, hard, day. From Richmond start at about 8:00 am which should have you going through Indianapolis from say 9:00 to 9:30, just after its morning rush hour. It would also put you in the Chicago area around 1:00 to 2:00 pm (depending on meal and other stops), well before Chicago's evening rush hour. You can let the whole thing slip as much as an hour later if that works better for you. Similarly, you could spend your overnight on the west side of Dayton OH rather than Richmond IN. That would even out your driving a bit better over the two days, and still let you miss the rush hours in the two major cities you have to traverse.

AZBuck