The child's happiness will raise over time, but if you want to raise it faster and train them a little at the same time, try using the green glove to praise them. Put them on their toys, sandbox, at the desk in the children's room or whatever task you want the kids doing and praise them with the green glove. After a few praises, the happiness meter will move to "Happy"

As for making the family clean up after a meal, it is a random act that you cannot make happen. However, if you use the green glove (again ) when you see them do it, they will be more likely to repeat that action in the future. Just be careful... I have overpraised one of my people in the past and they would start cleaning up before anyone had even sat down