Taxi or driving yourself are going to be the easiest way. Disney transportation can be a pain. You can either take a bus to AK and then transfer over to AKL (probably the quickest way using Disney transportation) or take the boat from the Swan to DHS and then transfer to an AKL bus. I would leave yourself a good hour in transportation time if your going to take the bus to AK and about 75 mins if your going to take the boat to DHS.
Usually $20 for a one-way fare to anywhere within Disney property. The number of people doesn't matter. At the Swan they have Mears Town Cars available but I'm not sure about the morning hours for a breakfast reservation. The Valet stand outside the Swan will help you arrange the transportation. As a warning make sure you get the fare price quote from the driver up front before you take off.