The mother in Lessing's short story "Through the Tunnel" is a single mom whose husband had died. Without a father figure in her son's life, she is left to raise her son as she sees fit, but also understands that she cannot fill the masculine void in Jerry's life. It is interesting to note that the question above asks what she could have done rather than what she would have done had she known about Jerry's activities on the other beach. The difference between could have and would have is great enough to produce completely different answers. For example, within the first few paragraphs of the story, the mother notices that Jerry isn't as content with her as he used to be. She senses that he wants to go exploring and allows him to go. She could have ignored his body language and not ask him if he wanted to go see another beach; but what did she do? She did ask him about his own desires and then gave him some freedom to exercise other choices. Hence, she allowed him to choose whether or not to return to the big beach with her or go back to the villa when he was done.
As for what she could have done when Jerry asked her to buy him some goggles immediately, she could have drilled him with questions about why he wanted them, but she didn't. The mother never inquired into any specifics after he had used the goggles, either, which she could have done. All she asked was, "Did you enjoy yourself?" Further, as concerned as any mother would have been, she could have gone back on her first impression to give him some freedom to explore and reeled him back into her, but she didn't.
In the end, the mother discovers Jerry's bump on his head and notices that he looks pale and she reminds herself not to fuss. When he tells her that he could hold his breath for two to three minutes, she doesn't overreact like she could have. She does suggest that he take a break from swimming that day, anticipating a "battle of wills," but he had done what he had set out to do, so that battle wasn't fought.