Final answer:
The provided texts do not specify an event where Sarah invites John, Sam, and Henri to a particular activity. Sarah is shown as a decisive and strong character who takes action to improve the living conditions for her family, but the details of the invitation in question are not included in the excerpts.
Step-by-step explanation:
The text does not specify an event where Sarah invites John, Sam, and Henri to do something specific. However, the texts do provide insights into Sarah's character and the actions she takes throughout different narratives. Sarah is depicted as a strong-willed and resourceful woman, in one instance leading her children to move their household into a new barn when she deems their old house unfit to live in. We see her instructing her children and assuming control of the situation, demonstrating her role as the matriarch of her family.
Throughout the various scenarios, Sarah shows resilience and an ability to take charge when necessary. Her actions speak volumes about her character and her willingness to make difficult decisions for the betterment of those she cares for. This information provides a broader context of Sarah's character but does not directly answer the given question as the event of inviting is not mentioned in the provided text excerpts.