@Oliver352 Your listing appears to have a maximum of 3 guests, so this family has not only misrepresented their group size but also exceeded your restrictions. You have the right to refuse them entry to your property on this basis, but Airbnb is unlikely to let you keep more than the first night's rate.
If you've already checked the guests in and left them behind in the apartment, your window of action is about to close, so you need to immediately decide whether you will allow this family to stay or not. If you wish to get out of the booking, alert your guests that you are unable to accommodate a group of their size, and get Airbnb on the phone right now. But don't frame that in terms of how "messy" the kids might be (even a single adult can make a big mess) but rather what your maximum occupancy is.
If you would rather let the guests stay on, there's not really anything you can do except note in your review that the guest lied about the group size. You don't have an Additional Guest Fee in your listing, so there's no point in asking them to pay more.
Remember, you are the boss of your home and your business, and it's solely up to you to take swift and decisive action when your rules and restrictions are violated.
