As always , insurance rules vary from state to state. Illinois has very specific rules from what I understand ( I dont work there so I am not sure what they are but they are consumer friendly). Parts usuage does vary from company to company also.
As far as your moms damages go , assuming she is using her own collision coverage , she is going to be bound by what her insurance contract says. The Framers appraiser isnt " required by company policy " to use any part - he is giving your mom what she paid for - collision coverage with the option to fix the car using parts including , but not limited to, OEM, used and aftermarket( this is the wording found in many standard auto policies). All well and good for those of us in the business but not good , obviously , for the average person who doesnt read their auto policy ( which everyone should just to be sure.
That being said , the alternative parts ( used and a/m ) , must be of like kind and quality. This means they must function and appear the same as an OEM from an insurance perspective. The problem with the entire arrangement is that most ( none that I know of ) define, legally, what " repaired to preaccident condition ( more policy wording) " means. They never use the word " restore" as restore vs repair have 2 seperate meanings.
For many older cars and most average consumers , they , on their own , can not tell and a/m part from an OEM. Can you list the parts they have down for a/m? If they fix your car with a/m , they will have to guarantee that part to be of the same quality/appearance. I would let them fix it with them , find something that doesnt look right, save the old damage parts to compare too and prove they are not of like kind and quality. One example is lights. Some have a difference in color or the internal reflectors inside. YOu can shine them on a wall and tell they don't have the same light pattern. Militant body shops will push how life endangering this is. Squeaky wheel gets the grease ( sad but it often comes down to this ). If you need any with IDing a/m flaws let me know.