What is a Permanent Solution to Hyperpigmentation from Chemical Peel?

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.

Once pigmentation has occurred, any sun exposure will cause additional darkening.  There is no permanent cure but it can be lightened.  Your mom's skin should be totally protected from the sun and treated lightly with chemical peels or lasers such as the Fraxel Re:store to prevent irritation which can cause more darkening.  Fading creams and sun protection are best during the sunny months.  Save the peels or laser treatments for non-sunny weather.  She should be assessed by a board certified dermatologist.  You should also protect your skin from the sun to prevent pigmentation in the future. 

This is a very tough problem for some people.  Unfortunately, she will have to stay on top of it by being extra careful with sun exposure.  She has what we call PIH (post-inflammatory hyperpigmentation).  She should not continue with the laser treatments, as these may be encouraging inflammation.  Bleaching creams and rigorous use of sun block are her best options.