You say the boat can only hold 2 people. And I don't count a dog as "people", don't know if he swims beside or if he sits in the servants lap or whatever. But he doesn't take up space.
If the servant and the dog is on the boat there is still room for one more person. So they will stay on the boat all the time.
First they ferry over one son at a time.
Then the father.
Then the mother.
Then the 2 daughters one at a time.
Then they step off at the other side too.
Am I right or is going against the rules cheating? :P