The sentence describes a general obligation or expectation for children to help clean up. The modal verb 'must' or 'has to' conveys this sense of obligation. 'Must' is often used for strong obligations or rules, while 'has to' can indicate external obligation. In this context, either could fit, but 'must' is a common choice for general rules or duties. 'Mustn't' implies prohibition, and 'doesn't have to' implies lack of obligation, neither of which fits the context of children helping to clean up.
The most appropriate choice is must.