Parents: What age you would allow you child to fly alone?

Okay, I am 15, and my little sister is 13. This summer, we have no plans, no camps, travel, plans with friends. Nothing. We really want to fly out to Alaska, from Boston with a layover in Seattle to visit our family out there. We would fly unaccompanied minors, and we have both made the route once before with our grandmother, who unfortunately will not be able to accompany us this time around. My dad has agreed, my family in Alaska is fine with it, but my mom doesn't think it is a good idea. She so worried about us having to make an emergency landing, or getting stuck in Seattle, or getting fogged out of Alaska. The flight attendants will be watching over us, so what can happen? We are both responsible, and know right from wrong. Please help, we really want to go!