Is Hyperpigmentation Due to Chemical Peel Permanent?

  In my opinion, the Hyperpigmentation after a chemical peel is NOT permanent.  Unfortunately, your mother may have a tendency toward this, as noted by one of my colleagues.  This may have nothing to do with the peel (and I recognize that neither I or anyone else may be able to convince you of this) and that she just has to be EXTREMELY careful with using sunscreen on these areas and avoiding excess sun exposure.

Sounds like your mom makes quite a bit of pigment on her own and I doubt that the prior peel is what the cause of this is now . Hormonal changes or changes in  or oral contraceptives might be changing the way she reacts to the sun but she probably has enough her own pigment for this to happen with small amounts of sun or inflammation anyway. She should apply sunscreen every morning and she might want to use a bleaching system when needed. Sunscreen is key!!

You are developing a post inflammatory hyperpigmentation.  Treatment for this type of problem includes the use of hydroquinone 4 to 8 %, Kojic acid, Retin-A, Topical steroid creams.  You can expect it to take up to 10 weeks for the pigmentation to clear. 
Also available from a compounding pharmacy is Klingman's formula which is a mixture of all of the above chemicals.