Recurrence in Stage IIIb triple negative breast cancer?

Yes, chemotherapy is known to be effective against triple negative cancer, especially if it's high grade (they typicallly are). Right now, it is the only systemic treatment available to us trip negs, as the hormone therapies that our ER/PR+ sisters get won't work on us. 

Diet and exercise are especially important for trip negs.  There have been threads on this - scroll down the topics here or do a search and they should pop up.  What's really exciting is that clinical trials have shown that a low-fat diet and vigorous exercise several times a week are especially effective for trip negs.  Risk of recurrence drop 30% or more.  So it's like an extra treatment for us that's perfectly safe and good for you.  

I don't know what the recurrence rates are for that particular stage and I understand your worry.  But remember, whether your mother's cancer recurs or not will be a 0 versus 100% reality and let's hope for the 0!.  It's true that trip negs have a higher rate of recurrence (than ER/PR+) in the first 3 years, but then the recurrence rates drop dramatically. 

Recognize too that most women get treatment and go on living their lives and may not frequent these boards.  So you may get some skewed results here.  However I know there are some threads here with survivor stories -- and I think your mom can get matched up through ACS with someone who had a similar diagnosis and has been through treatment and beyond.  That may be helpful too.