How is Jerry's growth and evolving maturity reflected in his relationship with his mother in "Through the Tunnel" by Doris Lessing?

In the beginning of the narrative of "Through the Tunnel," Jerry stays close to his mother, asking permission to part from her, then returning to her after going to the rocky bay; later, he demands goggles and goes independently to the rocky bay.
Dependence upon his mother
Because his mother is a widow and Jerry an only child, she is protective of her son; likewise, Jerry feels emotionally tied to her. At the beach, when she feels that he is not with her, she quickly turns around,

"Oh, there you are, Jerry!" ....Contrition sent him running back to her, And yet, as he ran, he looked back over his shoulder at the wild bay; and all morning...he was thinking of it." 

As Jerry's yearning to explore the rocky bay waxes, his mother senses that she may be keeping him too close to her now that he is eleven years old. So, although she is anxious, she gives Jerry permission to go the big beach. Jerry is excited to go, but still turns to find his mother on the beach:

When he was so far out...he floated on the buoyant surface and looked for his mother.

A burgeoning independence
After his experiences with the boys who swim under the water and rebuff him, Jerry swims back to the other beach and returns to the villa where he and his mother are staying. He waits for her, and as soon as his mother enters, Jerry demands swimming goggles, "pant[ing], defiant, and beseeching." She agrees, but he "nagged and pestered" her until she takes him to a shop. Then, Jerry grabs the goggles and runs off without asking permission.
As quickly as he can, Jerry swims to the big barrier rock. Adjusting his goggles on his face, Jerry dives into the deep water. However, the force of the dive knocks his goggles out of place; so, he fills his lungs and adjusts his goggles in order to see below.
Jerry explores the rock and finds the hole. Then, he practices and practices until he feels dizzy. But, when his nose bleeds that night, his mother cautions him and insists that he accompany her the next day.

It was a torment to him to waste a day of his careful self-training, but he stayed with her...[where it] now seemed a place for small children....It was not his beach.

Independence from his mother and a new maturity
The next day, Jerry does not ask permission to go to "his beach." Instead, he leaves before his mother has time to consider the "complicated rights and wrongs of the matter." When he arrives at the wild bay, Jerry ponders trying to go through the tunnel, but "[A] curious, most unchildlike persistence, a controlled impatience" leads him to wait.
After his mother tells Jerry that they must return home in four days, Jerry realizes that he must attempt to swim through the tunnel "if it killed him." So, he dives down, controlling himself, but feeling panic along with a sense of victory that he is moving through the tunnel. He knows that he must continue or he will drown. Finally, Jerry reaches the surface, although he feels that he may not be able to swim back to the rock. Yet, he manages, and when he removes his goggles, they are filled with blood.In a little while, Jerry returns to the shore and makes his way up the path to the villa. He rushes to the bathroom to wash away the blood and the tear stains, but his mother senses that Jerry is too pale under his suntan. "How did you bang your head?" she asks him, while at the same time warning herself not to worry. Jerry only tells her that he can remain under water for three minutes, at least. Moreover, "it was no longer of the least importance to go to the bay" as he has already completed his rite of passage.