No hotel shuttle needed. Just follow the signs toward Terminal 2 E and F gates, going to your left a bit at the top of the escalators out of the train platform. You turn right toward that part of the airport and the Hilton basement level entrance is right there, on the left at the Hilton business center. You don't go outside and there's absolutely no need for a hotel shuttle bus (not does the Hilton provide a shuttle bus AFAIK). The Hilton is located right at the airport, on airport property, and attached to the airport terminal. From the train to the Hilton is a two minute walk, absolutely no problem with wheeled bags.

You could take some bags to the Hilton during the afternoon and check in, then return downtown and meet wife for dinner before going together to the Hilton for the night. On the CTA trains, it costs $10 (plus $5 for the card if you don't already have one) for a day pass that entitles you to ride all rail lines, including to/from ORD, as many times as you want during the day. Otherwise, one ride costs $5 from ORD and $2.25 otherwise IIRC.

If you do take the train to ORD with luggage, try to avoid stations that require you to use stairs. From many hotels, IIRC Clark/Lake is very good, while the Lake/Washington indoor transfer (walking through a shopping mall) between red (Magnificant MIle) and blue (ORD) lines has escalator up but somewhat steep and narrow stairs down in both directions. Transit maps indicate which stations are accessible, which seems to mean that they have elevators for the handicapped. Including waiting, I'd allow about an hour between most of downtown and ORD.