Final answer:
The information required to answer what Aunt Cecile offered to do with Ty'ree and Lafayette after their mother's death is not provided in the given excerpts, so an accurate answer cannot be given.
Step-by-step explanation:
Unfortunately, the provided excerpts do not contain the information required to answer the specific question about what Aunt Cecile offered to do with Ty’ree and Lafayette after their mother’s death. Since the necessary context or background from the story is not available in the given texts, and no book or story title is provided either, it is not possible to give an accurate and meaningful response to the student's question.