When everything goes smoothly and your au pair ends his/her legal stay with you then parting companies is a sad moment. But for many other reasons you may want to end your agreement with your au pair. This is not something unusual. However, it is better if you do it properly and part companies in a civilized manner.
Usually you are required to give at least two weeks notice before asking her/him to go.
Very nice of you is to let the au pair to know when you think that something doesn’t work.