Final answer:
For a child with hypotonia and poor sitting balance, gentle rocking on a large diameter ball can effectively strengthen core muscles and facilitate active trunk extension, setting a foundation for improved motor control and balance.
Step-by-step explanation:
The most beneficial activity to include in the initial intervention for facilitating a 6-year-old child's active trunk extension, who has hypotonia and poor sitting balance, would be gentle rocking on a 22-inch (56 cm) diameter ball in a supine position.
This exercise can help in strengthening the core muscles, improving balance, and stimulating the vestibular system, which is responsible for spatial orientation and balance. Activities like rolling in a barrel could be beneficial later, but initially, the controlled movement of gentle rocking is more likely to help with trunk extension without overwhelming the child's motor control abilities.