Trading in a new car?

I bought a new Mazda 3 i sport sedan 2012 in New Mexico and after a few days I just simply regret it because I really wanted the i touring at first. I got the sport for 16k. The touring is about 19k. I had been trying hard to return it in the first week but they simply refused it. I even contact base legal office (I am in the military) and they said there's nothing they can do about it. I called another dealership to see what they can do and they estimated 13-14k for me to trade in and buy the touring, so I would have to take a loss of about 2k+ in this deal, and I am assuming I probably have to pay for title and registration again, so my loss might be 3k+. Not sure though how they do this.

I wanted the touring simply because it has the skyactiv engine, and it comes with enough options to make it worth it. I can probably save enough gas money in 10-15 yrs to offset the loss I take. I am going to visit this dealership tomorrow and ask for more details. I had been doing research on this for a few weeks now so I am pretty desperate at this point. Hope someone can give me good advice.