In "Through the Tunnel," Jerry's mother allows him to explore the bay because she recognizes that he is at an age where it is appropriate that he be granted more freedom and also because she doesn't want him to feel smothered by her attention. When eleven year-old Jerry takes her up on her offer to allow him to go to the bay, alone, she thinks,
Of course he's old enough to be safe without me. Have I been keeping him too close? He mustn't feel he ought to be with me. I must be careful [....]. She was determined to be neither possessive nor lacking in devotion.
This is basically the quintessential parental dilemma. Jerry's mother worries about giving him too much freedom, but, on the other hand, she also worries about not giving him enough freedom. If she gives him too much, then he might not be safe. It she doesn't give him enough, then he might feel resentful of her and grow distant. Thus, she decides to allow him to go to the bay, day after day, without her in order to prevent his feeling that she is "possessive" of him.