Translation:They allow children to help clean.
You can say "ze sprzątaniem" or "przy sprzątaniu", but yeah, close enough. Added.
btw how come you can have 2 infinitives here, or is it only with future tense that it can't work?
I don't really know. This sentence doesn't strike me as wrong, but I guess it probably would be safer to avoid this double infinitive by saying e.g. "pomagać w sprzątaniu" or "pomagać ze sprzątaniem".
well the version I tried didn't work... can you check whether all possible versions that work with allow also do with let
You wrote "they let kids to help clean". You don't use "to" with "let". But you do that with "allow" and "permit".
(I generally don't know who reported what, but there's not many reports and there's such a report from 5 days ago, so it must be yours)