In The Way to Rainy Mountain, the story of Grandmother Spider and her adopted child is one of the Kiowa myths retold by Momaday, in the same oral tradition that the Kiowa have always passed down their stories and history.
Grandmother Spider is worried about the Sun's child because she knows how powerful he is, as a diving being, and worries that she will not be able to control any aspect of his behavior. His constant disobedience shows how right she was. For instance, he throws a wheel into the sky after warnings from Grandmother Spider, and this ends with him being cut in two pieces, each of which reforms into a "twin" of the other. Grandmother Spider now has two disobedient children to raise.
Her fears that she cannot keep the twins safe and raise them the way she should continue to be confirmed as they play a game which involves throwing their rings into a giant's cave. However, when they are nearly injured or killed by the giant, they remember their adopted mother's words for once and are able to say an incantation she taught them to save themselves.
Despite Grandmother Spider's fears, the twins are said to have lived long and happy lives, even after her death. Perhaps she taught them well enough after all.