Hi Sue
Normally, there are two reasons that anyone of the same family is picking on another. The first reason may be that both cygnets are males and there is a sibling rivalry.
The second reason may be that something is wrong with the cygnet that is being harrassed. It is normal in nature to try to banish a sick or injured member to prevent disease from spreading to the entire flock or being subjected to predation.
The key to your situation is to watch the parent swans. If they are still allowing the chased cygnet to feed and stay with the family, then we would not worry too much and let the rivalry play out as long as no one gets hurt.
Is the swan that is being chased the younger sibling or the runt of the brood? This again, would be somewhat normal behavior as most younger siblings get picked on by older siblings. We hope this information is of benifit. The Regal Swan