damn man sounds like you've got the chain around your neck like a dog. I was out fucking climbing shit with people my parents only kind of knew when I was like 14, and they thoroughly encouraged it.
I would just try to sit down with them, and try to get them to be as specific about their specific concerns about your proposed trip. This generally doesn't work since most parents are stubborn as shit, but even so, it may give you some insight into future plans you may have. If they do start to open up, you can try to alleviate their concerns and inhibitions, especially if you work out an agreement of trust based on some mutual parameters. I was able to convince my parents to let me miss school for two weeks to go skiing (in a school that attempts to withhold credit after only 3 abcenses) because i did all the research I needed. Granted, that was a very wild circumstance, but I was able to disarm their misconceptions.
Do make them realize, cautiously and with respect, that you will be 18 before they know it, and your ability to make decisions will heavily rely on your experiences, and not necessarily their guidance. A trip can be beneficial in several ways. It builds up your ability to handle situations as well as just experience life. It also provides an opportunity to build their trust in you.