How to complete the Clean Your Room duty in Disney Dreamlight Valley

During the Cheshire Cat Chaos event in Disney Dreamlight Valley, you'll have the opportunity to complete four separate dreamlight duties in return for some limited rewards. The Clean Your Room duty is one of the four, and the most challenging since you'll have to travel between the valley and a separate realm in order to complete it.

You'll need access to the Toy Story realm, and both Woody and Buzz unlocked before you can complete this duty. Provided you've already done this, you'll be...