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.