Unfortunately, this is normal swan behavior. The one way to intervene is to get someone with wildlife rescue expertise to try and capture the new family and relocate them to another pond further away from your area. This relocation may be difficult if you live in a state where wildlife officials want to kill all Mute Swans in order to introduce thd larger Trumpeter Swans for Trophy Waterfowl hunting.
If you cannot get someone to capture and relocate (you need to inquire very cautiously so as not to alert wildlife officials to your area), then there is another alternative. You or someone need to get a boat–Not a kayak or rowboat, but a large enough boat to get between the two families and slowly chase the new family away from the island and back towards the direction that they came. You will need to be very cautious so that the male swan does not hurt anyone in the boat should he become defensive and that he or his family does not get hurt. That is the reason for a fairly large boat. You may have to harrass him consistently to get him to move his family which could take a couple of hours and even days. Understand that he us also trying to find a safe territory for his family as he may have been threatened and removed from his original habit. We are approaching September, which is the time for migration, and many swan families are trying to teach their young how to fly for migration and they need a fairly large area for flying. If your area has a clear area for takeoff and landing, this may be the reason why the new family appeared. If the new cygnet family can fly, harrassment may cause them to leave quicker as the parents will take them away. If the cygnets from the new family cannot fly, the male may be looking for another area for better food resources or safety from predators. The key to all of this is to find out why they left their area. If you can tell me what area you live (state and city), we might have a contact in your area that can help. The Regal Swan