The turning point in a story is a moment of significant change (usually for the main character). After this point, things are significantly different. In regard to "Raymond's Run," the turning point of the story is most definitely when Squeaky notices Raymond running along the sidelines of her Mayday race.
Why is Raymond's run along the sidelines the turning point? Because Squeaky, as the main character, changes at that very moment: Squeaky changes from being selfish to being compassionate. Squeaky changes from looking only toward herself for wins to looking towards coaching her brother towards wins. Before the turning point, Squeaky is focused, selfishly, on her own running. She is continually keeping her eye on the new girl, Gretchen, in scoping out her abilities. At this time, Squeaky's main focus is winning the Mayday race.
As Squeaky runs the race, she notices her older brother (who has some learning differences and disabilities) supporting her grandly by running along the sidelines. It is at this moment that a light bulb goes on in Squeaky's mind. Her focus immediately switches. Right in the middle of the race, Squeaky is no longer concerned about winning; instead she begins focusing on how to coach her brother to be a good runner. Even when the winner is announced, Squeaky is already in the midst of her reverie. She hardly hears the announcement: Squeaky has won the race. However, Squeaky has "won" a lot more: a compassionate focus over a selfish focus.
In conclusion, it is also important to note that this turning point also is alluded to in the title of the story. The title says nothing about Squeaky, but only about Raymond. This first run of Raymond's inspires Squeaky. It is for this reason that it surely is the turning point.