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.

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.

Hypopigementation is a permanent skin condition.  Once the melanocytes is damaged there is no way to correct it.  You can cover the spot with makeup to blend the spot into the skin tone around it.

"Dr.D"

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!!

Pigmentation is due to genetic tendencies, sun exposure and hormones.  Both thyroid problems and estrogen imbalance can cause exaggerated hyperpigmentation in susceptible individuals.  I think you need to see a cosmetic dermatologist who understands hormone metabolism.  Have you been told if the pigmentation is in the epidermis, the dermis or both?  This is an important question to ask your physician.  The only laser I have had success with in treating hyperpigmentation reliably is the 532nM KTP laser.  You MUST wear sunblock every single day - and I'd suggest one that is a physical block only, since sub-clinical inflammation (often from chemicals in sunscreens) can potentiate the hyperpigmentation.  Good luck!