There are only two plausible explanations. One is that the family found a stream that is not visible from the air, a culvert or any other type of land/water access from one pond to another. Two miles is not a long way for birds or animals. Swans can walk or swim long distances in a few hours. Swans can carry their cygnets on their backs, so if the mother was walking or swimming, she could have carried the cygnet on her back. It is not plausible that she carried the cygnet in her mouth, especially during flight because the propensity for dropping the cygnet would be extremely great. The same goes for carrying the cygnet on her back during flight, so she would have to carry the young bird when swimming or walking.

The only other plausible explanation is that the male has two families. Yes, this has occurred and has been documented in swans. Usually, swans will mate for life, but there have been instances where they have re-paired, especially if the first pairing was unsuccessful in producing young. So, you may not have seen the first nest in your pond, as it could have been secluded on the edge of the woods. We have seen swans nest 3-5 feet inside a wood line as long as there was access to a pond/lake/stream.

The above scenarios are the only ones that we can think of that would fit what your parents are observing. We would go with the scenario in which there was water access not visible from the air in dense vegetation. If there was a problem with the nesting habitat such as the presence of predators, lack of food or water resources, etc., then the parents may have felt an immediate need to move the cygnet into a more familiar, secure and suitable habitat, hence your pond. The Regal Swan