At ORD each car rental agency has its own lot, so each company drives their own shuttle buses. When you get out of T1, go to the outermost traffic lane and you'll see shuttle buses coming and going from different rental agencies.
Since you don't need your wife to be named on the contract, consider to let her wait with your child and baggage while you get the rental car, then drive back into T1 arrivals area and you can load up curbside.