It should be enough time, but wait times can be long, so it's difficult to predict exactly how rushed you may find it.
In terms of the procedure, you'll exit the plane, and proceed through a series of corridors to immigration. You'll go through immigration control (you can check historic wait times for this part of the process to get an idea of how long it will take), then end up in a baggage claim area. You'll claim your checked bag, and take it out through customs. At the customs exit, an airline representative will take your checked bag back, and it will be checked in again to Chicago (there's no need to wait again for this step, your bag is already tagged, just a quick drop-off). From there, you'll follow the signs to the AirTrain, a small monorail that runs between terminals. Ride that for a few minutes to Terminal C (or wherever your flight departs from, monitors will guide you). From there, you'll go through TSA airport security (Star Alliance Gold should get you priority here), and walk to your gate.
All international->domestic connections require that you go through TSA security, so the post-security transfer shuttle bus does not apply in this case.
If you don't make your connection, United will put you on the next flight with space to Chicago. United has 8+ flights from Newark to Chicago a day, so the worst case scenario should be an unexpectedly long wait for a later flight.
Depending on how comfortable your mother is with traveling long distances, you could consider requesting electric cart/wheelchair assistance from the airline (it's free and very common at US airports). That will help your mother navigate this entire process (there's a fairly significant amount of walking and waiting in lines involved) and will likely help expedite your passage through immigration and security lines.