Okay, as a guy that likes to run away from his family at least once a year, I'm going to give you serious advice.
First you need to honestly talk to her about why you want to travel by yourself. Early on I told my wife that sometimes I just need to be on my own. It doesn't have anything to do with her, or how I feel about her. It's who I am as a person. I love her and my kids more than anything in the world, but there is a part of me that needs to get away from everyone and decompress from life. It's not about escaping from the marriage, because I'm still completely committed to her and our family, and I'm not going out there to cheat on her. It's my way of having time to be with me. That's healthy.
You may be in a bad spot right now because it sounds like you didn't establish this at the beginning of your relationship, and she may not understand why all of a sudden you're feeling this way. Tell her what you're feeling, but don't expect her to pull a 180 right away. This will probably take a while to get her to understand. Be patient and try to understand why she feels the way she does too.
You've got to start small. Wean her into it. Start with day trips. Work your way up to an overnight. Then work up to a long weekend. Do this for a while, and she'll get used to you being away for a couple of days. Don't go straight into disappearing for two weeks. It's like trying to get her into anal. If you try to just stick it in her butt without any prior experience and she's going to be very unhappy. You need to work your way up to it.
In your case it seems like your wife is also against the idea because she's jealous you're going to go do something she can't. It's important that you take her places as well. Don't leave her completely high and dry, and understand that she probably wants to be able to go out and see and experience the same things you do. Make sure you balance out your travel.