Writing a story with thirty children has an obvious failure mode: everyone contributes and the result is a shapeless list of everything anyone shouted out. The fix is not to take control back. It is to be deliberate about which decisions you hand over.
One: hand over the character, keep the structure
Character decisions are ideal for a group — who this is, what they look like, what they always carry. They are concrete, everyone has an opinion, and no individual answer can break the story.
Structure decisions are not. Whether the problem gets solved on page four or page nine is a craft judgement that a vote will get wrong. Hold that one yourself, and nobody will notice you did.
Two: use constrained choices, not open questions
"What happens next?" produces chaos. "Does she go into the woods, or does she wait by the gate?" produces a decision. Two or three concrete options, both of which you would be happy to write, keeps the story on its feet and still leaves the class genuinely in charge.
This is also how you avoid the moment where a child suggests something wonderful that would take the story somewhere you cannot follow. If the options are yours, every outcome is one you can write.
Three: give the quiet decisions away
The loud decisions get grabbed by whoever speaks first. The interesting ones often do not. What is the weather. What is in the character's pocket. What does the room smell like. What is the one word this character always says.
Assign these to individuals rather than putting them to the room. A child who chose the weather has a stake in every page, and it costs you nothing structurally.
Four: let the pictures carry the disagreements
When two suggestions are both good and incompatible, you can sometimes keep both by putting one in the text and one in the illustration. The story says she walked to school; the picture has the dog that half the class wanted, following three steps behind.
Children notice this and are delighted by it, and it teaches something true about picture books: the words and the pictures are allowed to tell slightly different stories.
Five: read it aloud before it is finished
Read the draft to the class while it is still rough. They will hear problems you cannot see — a page that drags, a name that is hard to say, a joke that does not land. Children are unsentimental editors of their own work, and they are usually right.
It also puts the finished book in a different category. It stops being an assignment and becomes something the class made, which is the whole point of doing it this way.