Why would Chopin have thought it important to include this detail in her brief mention of the children's nurse ?

I assume you're referring to the "detail" of the
children's nurse being a quadroon.  Kate Chopin's The Awakening
begins as the family is vacationing in the Grand Isles and nearly all the rest of the
story is set in New Orleans.  This is a Creole world, and a quadroon (a person who is
three fourths Caucasian and one fourth Black) would not have been
exceptional--especially as part of the serving class.  In fact,most quadroon women at
this time were relegated to domestic work of some
kind. 

Another reason she may have mentioned it was to add
to the social commentary of the novel.  Class distinction is a major component of this
work; adding a quadroon children's nurse who stands in the background but is still more
of a mother than their own mother speaks volumes. 

Chopin's
mention of that detail is not particularly surprising, given the location, the time, and
the social commentary of this novel.