Beverly,
Many of our family stories are just that - Stories. Quite of bit of your story is implausible and was probably embellished as time went on.
You state they went 3000 miles. 3000 miles from where? I ran some facts. Hawaii is 2,390 miles from California; 3,850 miles from Japan; 4,900 miles from China; and 5,280 miles from the Philippines. 3000 miles from the Hawaii islands is from nowhere. Your story is not 3000 miles. If the story is true, someone has embellished it (my Civil War ancestor was shot 44 times and only 1 bullet hit his belt buckle. Again, it's implausible. He was probably shot at only 4 times and the story took on a life of its own after all these years). And then you have your floating part. I checked around and found a news article about a British guy who rowed across the ocean (I'm guessing the Atlantic - he's British). It took him 59 days to ROW the 3000 miles. He was stocked with food and water. If your story is true, floating would take more than 2 months. Everyone would have died because they would not have had enough food and water to survive that long. An Internet search pulled up a human can go 3 weeks without food, but only 3 days without water (yes, there have been reports of some people surviving a week or a little more without water).
So now that I've pulled up facts, what part of the story is true? Maybe just the bare bones. A few men took off after the whale and became separated from the main whaling ship. They floated for what seemed like miles (and that's how your 3000 snuck in) and wound up on Molokai. Only 2 brothers survived. Or maybe none of the story is true. Children are very naive. I was probably about 6 when I realized that when my sister had a birthday, a week later, my dad had a birthday. Then in June, I had a birthday and a week later, my mom had a birthday. So I asked my mom why. She said it was because my sister was my dad's birthday present (just a little early) and I was my mom's birthday present (just a little early). So we were birthday babies. I believed that at face value. After all, my mom said it, so it must be true. In the summer, we were playing with the little neighbor girl. Her big sister came to pick her up, because she was going home to celebrate her birthday. I asked whose birthday baby she was. The big sister looked at me like I was crazy. So I explained. She said it didn't work that way in her family. I was shocked. I though all families had kids for birthday presents. After all, my mom said so. My dad said things as well. One time, as we were driving somewhere, I asked my dad how did he know how to drive to Disneyland (I'm from southern California). He saw a billboard sign coming up. He pointed at it and said, "You see those signs? You just follow them." I believed that until I was a teenager and learned how to drive. My dad had said it. So it must be true. (Thinking back, now as an adult, my mom may have been in the middle of something and just made up an answer so I would go away and play. My dad may have been listening to a program on the radio and wanted me to be quiet in the car so he came up with me watching the signs as we drove down the freeway).
Professor Edgar Knowlton is now deceased and may not have known about DNA testing for genealogy. Since your family story has a lot of story to it and not a whole lot to verify, you will have to turn to DNA to figure out where that line came from. As I said in my original post, Pico is starting to form pockets. For some people, we are able to tell where they came from. For others, we can't tell - not yet. But we will be able to tell as more and more people DNA test. You will want to test the person who is the oldest generation and the closest in time to the 2 men in your story. That person may be a great-aunt, a parent, or maybe it's you. Maybe you will get lucky and hit a pocket of people who have tested from a particular freguesia. Maybe you will be like the majority and have to play wait and see. Either way, you'll have to leave that story as a story and move on and the only way to do that is with science and DNA. The DNA test you want is on sale now for $69 instead of $89 (add $12.95 S&H - includes return postage for those residing in the U.S.) You can order from
www.ftdna.com. After you order, join the Azores DNA Project. You can email me after ordering and I can tell you how to join a project (you may join multiple projects, such as the Polynesia DNA Project or any other project you qualify for).