Jerry's mother is worried that she might be overprotective. She allows him to go to the other beach alone. Since this story is all about growing up, it is an important first step that Jerry is allowed to go somewhere alone, enabling him to be more grown-up. She also has more trust in Jerry, a sign that Jerry's transformation has begun. She purchases swim goggles without demanding why he needs them. This event especially advances the plot of the story because it builds toward the main event of the whole story: swimming through the tunnel, Had Jerry's mother refused to buy the swim goggles, he wouldn't have been able to swim through the tunnel.
Through the course of the story, we don't see Jerry's mom as someone who hovers around Jerry. It is implied that she is able to recognize that Jerry is able to self-motivate himself and provides him with certain freedoms. In the scene wherein she initiates the conversation of Jerry going to a different beach, as opposed to staying on the "safe beach" as usual, she offers him the opportunity to decide for himself, and when Jerry decides to play by the rocks, she allows him to be independent. Jerry's mom worries about "keeping him too close to her" as she's the only one raising him. In this way, her motivation to be a better mother in terms of offering opportunities for him to grow and be independent. Her way of motivating Jerry, albeit unconventional for some, can be what pushes him to pursue his rite of passage through the tunnel.
