Jerry's mother is motivated by her concern that she give Jerry enough freedom, freedom appropriate to a quickly-maturing eleven-year-old boy, but not too much, as too much freedom might be dangerous. "She was determined to be neither possessive nor lacking in devotion." She doesn't want to smother him with her attention, but she also wants to protect him from anything that could be harmful to him. Further, she doesn't want Jerry to think that she doesn't care about him.
Her motivations help to drive the story because, were it not for her scrupulous attention to his behaviors, Jerry would likely not have even gone to the bay. He doesn't ask her at first if he can go because he doesn't want to hurt her feelings (he is keenly aware of her concerns); it is she who notices his thoughtful gaze toward the "wild bay," and she who offers him the opportunity to go there. Further, it is her desire to grant him independence that enables him to go day after day, even when she notices that he looks like he's "overdoing" it. Without her fairly typical concern and her recognition of his age-appropriate desire to have some independence, Jerry would never have gone to the wild bay and witnessed the older boys swimming through the tunnel.