E.S.
Do they act the same way in the daycare? If they don't it might be because they know there are rules to follow, like picking up the toys and not destroying property. Since you work there you know what the rules for the children are so if they are working out for them at the daycare try them at home. It is rare case when a three year old will clean up after herself/himself, but that doesn't mean you stop telling them too. I have said this before and I will keep on saying it- Parents set the rules, children follow them not the other way around, and if they don't there should be consequences.
I too have a three year old and she really dislikes picking up her toys, but she has learn it is best to do so if she want's to see them again( they magically dissapear).