We have never seen a mother swan carry a baby swan in her mouth or on her back while flying.

Obviously, she has found a way to get them to your pond. So, there are only two plausible theories.

One would be that she has placed them on her back and walked the entire way, as swans can cover a lot of ground quickly while walking especially if they know a shortcut. There is also the possibility that there is a stream that you cannot see from the air and also one so small that most people do not know exists and she floated/swam to an area near your pond, and then walked the rest of the way.

We suppose she could have possibly flown with the cygnets on her back, but unless they were somehow buried in feathers way on top of her body and under a portion of the wing that does not open during take-off, landing or flight, we can't see how they would remain on the mother's back without falling off. In any case, we are glad the family is intact and made it safely to your pond. The Regal Swan