This is normal behavior as the parents are starting to chase the young from the habitat prior to the next nesting season. More than likely, the cygnet sitting in your yard is a young male and the parents are viewing him as a potential mating rival and want him gone ASAP. The other cygnet is probably female and is not seen as such an immediate threat. Regardless, both cygnets will be chased and encouraged to go find other juveniles so they can find a future mate and habitat to start their own family.

Offspring may misbehave or throw tantrums, but nature does not allow such bad behavior and it is dealt with swiftly and severely to discourage non-conformance which could lead to the death of the individual member, the family or entire flock. The Regal Swan