If she can walk she might want to get out of the chair and walk thru the metal detector. Just make sure she is not wearing anything that would set off the alarm. If she would rather stay in the chair then she has a few options.
Here is a link to the section of the TSA website outlining the options. Hopefully it works. If for some reason there is a problem getting thru the check point you can always request it be resolved in a private location. That makes it easier for your MIL. One other suggestion. Before you even get to the airport, approach the whole screening process as an adventure. Think of some silly scenarios of what might happen and have a good laugh over it. Then if problems do pop up at the check point maybe your MIL will see it as another silly scenario and be amused rather than distraught.