The answer to this question can be found in the chapter titled "Enter April." It is chapter two. Chapter two functions as a bit of a flashback because chapter one is about the Professor watching the kids play the Egypt Game. Chapter two explains how April came to the neighborhood even though her mother lives in Hollywood. We are told very early in the chapter that April's mother is very "glamorous" and sent April away to live with a grandmother she hardly knows.

She came because she had been sent away by Dorothea, her beautiful and glamorous mother . . .

April assumes that she won't be with her grandmother very long, so she doesn't have a very good attitude about the entire situation; however, the grandmother knows better. She knows that Dorothea's career puts her on tour quite often, and as her success increases, her time away from home will also increase. Dorothea is more focused on her career than her daughter, so she sent April to live with April's grandmother.

Dorothea had promised it would only be for a little while. Only until
things got more settled down and she wasn’t on tour so much of the time.

April is sent by her mother to live with her paternal grandmother at the Casa Rosada. 

April's "beautiful and glamorous mother", Dorothea, is a single parent and an actress.  She is on tour a lot, and essentially doesn't have time for her daughter, so she sends April to live "with a grandmother she hardly (knows)".  Dorothea has promised that "it (will) only be for a little while...only until things (get) more settled down and she (isn't) on tour so much of the time", but there are clues that April's time at Casa Rosada will be of an indefinite length.  Her grandmother, who used to live "in a tiny super-modern apartment, like a cell", has moved to Casa Rosada specifically "so that (April) (can) have a bedroom of her own", and, although she has promised otherwise, Dorothea rarely calls or writes (Chapter 2).