This particular writing prompt is fairly wide open for you to tackle in just about any way that you see fit. The only limitation is that the story's events need to still occur. That means you still have to have a confrontation with Squeaky. The race still has to happen, and Squeaky still needs to win.
The rest of it is almost entirely up to you. Giving Gretchen siblings is a good idea because that gives her common ground with Squeaky in an area other than running and sports. I would have her live in the same general area as Squeaky too. These races and this get together are a part of a community event. It is not a statewide competition, nor is it a competition between different schools.
I don't recommend making Gretchen humble. I would make her just as aggressive, hard working, and cocky as Squeaky. The text supports this attitude because Squeaky tells readers that Gretchen has been bragging about how well she is going to do in the races.
I’m the fastest and that goes for Gretchen, too, who has put out the tale that she is going to win the first-place medal this year.
Since the story is going to be retold from Gretchen's point of view, I would make sure to have some sections in there where she tells readers about Squeaky. Don't be kind to Squeaky either. Squeaky is the undefeated running enemy that Gretchen plans to finally dethrone this year. Explain to readers why this is going to be the year that Squeaky finally loses. You could play around with the idea of having Gretchen know all about Squeaky's training runs, and have Gretchen be training even harder and more often.
You could end the story with her being shocked and dismayed at having lost, but I would end your version in a similar fashion to the original. Gretchen and Squeaky see each other as equals and worthy competitors.