You shouldn't have any problem to check bags to their final destination, at least for your family. For you, it might need more negociation, especially if you're departing apart from your family, but it's definitely possible. Make sure to be checked in for all your flights.

No storage in ORD and Hilton (and any hotels) will usually refuse to check if you don't stay there. Union Station has a bag check but you need a train ticket.

You may want to look at bagnb.com