I wonder whether we can discuss Hazel's "initiation" by refering to the way in which she learns a very hard lesson about adults and how they relate to children. Let us recall that the central action of the story revolves around the way in which Hazel was expecting to see a film but the cinema puts another film on instead. Hazel as a result stirs up something of a revolt and demands a refund, then going on to commit arson when she is refused, shutting down the cinema for a week. Hazel avoids punishment by pointing out the injustice of the situation. The adults had made a promise and then broke it, which represented an unforgiveable act in the eyes of Hazel.
In the same way, in the car with her uncle, Hazel once again sees ample proof that adults cannot be trusted when they make promises to children. Her uncle had promised to marry her when she was little, but now he is marrying somebody else. Hazel's initiation therefore concerns her understanding of the way that adults will lie to children to suit their own needs, and don't even feel the need to apologise.
There are certain indicators within a text to symbolize an initiation process, like the change of a name, a journey etc. In the case of Hazel one can find especially the name change theme (when she insists on being called by her full name) and also the journey motif (trip to south - especially meaningful as it is a black girl who experiences a initiating moment). However, the story is an example of an uncompleted initiation story - one can't really tell in what way Hazel is affected by her experiences. At the end she remains confused and puzzeled so she is not able (at that point) to realizes the differences between the meaning of irony and real talk which still marks her as a child. She is on her way but does not experience the full initiation within the stoy.
Have written my final paper about this (unfortunately in German).
A good introduction to the Initiation motif in literature is Peter Freese.
I hope I could help you! Katja