The swans feel extremely safe and comfortable in your back yard. There are no domesticated or wild predators (dogs, cats, coyotes, etc.). So, of course they are going to sun themselves in your yard. You probably have a nice green plush lawn unlike other yards in the area.

Once the cygnets are fully grown and the parents tell them to get lost, the parents and the cygnets will begin to explore other areas of the lake and you will have your yard back.

You can expedite the matter, but you must be really careful so that the swans do not get hurt. You can leash your dogs, allow them to bark and walk within the area of the swans but not too close. You do not want to hurt the swans. You can also chase the swans from your backyard.

In doing this, you may make the swans uncomfortable, but you may chase them from your area forever and they may go into an area that is not a safe as yours. So, if you do not want to ever have swans in your backyard, you can make them uncomfortable, but there may be a cost in that they will never trust you or your area again. The Regal Swan