Describe the relationship between Jerry and his mother at the beginning of the story "Through the Tunnel."

The relationship between Jerry and his mother at the beginning of the story is pretty typical of children at Jerry's age (eleven) and their parents.  His mother is conflicted about how much freedom she ought to allow him: she doesn't want to smother him but neither is she ready to give him complete independence.  When he expresses a wish to go to the "wild bay" alone, rather than with her to their usual "safe beach,"...

The relationship between Jerry and his mother at the beginning of the story is pretty typical of children at Jerry's age (eleven) and their parents.  His mother is conflicted about how much freedom she ought to allow him: she doesn't want to smother him but neither is she ready to give him complete independence.  When he expresses a wish to go to the "wild bay" alone, rather than with her to their usual "safe beach," 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.

Like most parents, she's torn about offering him the freedom he needs in order to become an adult.  She wants to protect him and keep him safe, and this becomes impossible if he achieves independence from her.

Moreover, Jerry feels conflicted about his mother, too.  On the one hand, he really wants his freedom, but he also feels obligated to her, perhaps because of her status as a widow.  He knows that she is alone without him, and so he first declines her offer of freedom, "smiling at her out of that unfailing impulse of contrition -- a sort of chivalry."  He knows he will feel guilty if he leaves her on her own.  He is later "lonely" without her, when he is in his "wild bay," looking at her on her regular beach.  Even by the end of the story, he still very much desires her attention and approval (despite the sense we get from his desire for the older boys' approval at the rock that her attention and approval will soon no longer be enough for him).