What's the Name of That Book??? discussion

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Rhapsody
SOLVED: Adult Fiction
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SOLVED. Fantasy Three (?) people found a cave system while being pursued by someone. They traveled through it for a long, long time, and traveled through the world, ending on the other side of the world, and centuries/milennia later [s]
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But now I'm thinking I should reread it. Despite the incredible Mary-Sue-ness, I bet I'd still love it.
The beginning of the story was roughly as follows: Three (?) people found a cave system while being pursued by someone. They traveled through it for a long, long time, and traveled through the world, ending on the other side of the world, and centuries/milennia later, even though it felt like a lot shorter to those people traveling through the world. Also, these three (?) people are for some reason remembered as outcasts, or maybe even traitors, for reasons unknown to them.
That is pretty much what I remember of the plot. Some other details: The homeland of the three (?) people was destroyed somehow and the people traveled to the other side of the world through the use of ships. Some people randomly travel through time in the book (apart from the three (?) people the story is mainly about). There was some kind of long-lived race/people in the book as well. And I seem to remember a dragon, but I have no idea what that had to do with the plot.
It may, or may not have been youth literature; I was about 13 when I read it, and I read both youth and adult literature at the time. I have absolutely no clue about title or author. Can anyone help me find it? :3