I realize I'm an Air Force guy however I believe USMA and USAFA (along with the other SA's) share similar visions for their candidates.
I would counsel you to go on the mission trip IF this is something that is important to you. And here's why I say this.
It may well be that "once in a lifetime opportunity" although truthfully, you will probably have other opportunities later in life. However taking this trip, overseas, and having to deal with all the unknowns, working with others that are very different from yourself, gaining experiences in the areas you will, would be highly valuable to your personal development and probably to you in helping shape your leadership model.
Girls State is HUGE...it's a high honor, looks great on the resume, etc...etc..
So does, IMHO, this: "Selected to attend Girls State 2014" and then the statement "Volunteered to serve a Church Mission in "NAME OF COUNTRY" to both aid the less fortunate, and to enhance my knowledge and personal development..."
Or words to that effect. I sit on my Senator's selection board and when I see things like this...I'm impressed because it shows a lot decision making and maturity.
Just my opnion; you have some great choices and opportunities ahead!
Best wishes!
Steve
USAFA ALO
USAFA '83