What an interesting question! Given what we know about Jerry's mother, we can use this information to help construct a character analysis of her.
At the very beginning of the story, Jerry's mother's naked arm is described as being "very white in the sun." The next day, Jerry observes her "bare arm, now slightly reddened form yesterday's sun." Primarily, nakedness (as used in this context) suggests vulnerability. Further, readers might also consider Jerry's mother's slight sunburn to be representative of a sort of weakness or vulnerability. Both suggestions seem to be consistent with other examples of characterization we can find for her.
As the story opens, readers are aware that Jerry's mother is a widow who worries and second-guesses herself frequently. She obsesses over whether or not her decision-making is beneficial for her son and whether her parenting has been effective. All of these qualities, on some level, suggest weakness or vulnerability. When Jerry's mother first (and briefly) loses track of her son, she is impatient:
She frowned, conscientiously worrying over what amusements he might secretly be longing for, which she had been too busy or too careless to imagine.
Then, when Jerry expresses a desire to venture down to the bay, his mother worries:
She was thinking. 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.
Again, her vulnerability to the sun might suggest a vulnerability in her character. Further evidence to support this idea can be found at the end of the story, after Jerry has successfully conquered the tunnel and his mother questions him about his day:
"Have a nice morning?" she asked, laying her hand on his warm brown shoulder a moment.
Here, Lessing creates the image of strength through her description of Jerry's shoulder by using the word "warm," as the shoulder is typically an indicator of physical strength (which Jerry needed to be able to accomplish his goal). However, in the next sentence, she observes, "You look a bit pale," which suggests weakness and contrasts Lessing's previous description of Jerry's coloring.
Again, great question. I'm not sure that there's a "right" answer, but as authors consciously include details like the references to Jerry's mother's arm, this is my best guess. Hope it helps!