Nice car! I really like them and hope they are successful in the market.
Based on what I sell that car for, and using $1500 down, and guessing on FL taxes and fees, your interest rate is about 15%. Not the worst I've seen but not great, either. It is what it is so no sense in worrying about it.
If I could make a couple suggestions as you plan for the future:
1. Absolutely make your car payments on time without fail. Same with all your other bills. Messing up your credit history now will hurt you for years and years. No mistakes here, ok?
2. Establish a relationship with USAA, Pen Fed, and/or NFCU immediately. Companies like USAA serve military folks very well and you should seriously consider doing all your personal banking with them. Having access to USAA and the others gives you a huge advantage over us civilians so def check them out ASAP.
3. Plan to re-finance the car loan in 12 mos time. I would recommend you make the minimum payment on the car loan and put any excess cash into a savings account (where????.....) to be used as a down payment at re-fi time. You will need that cash. A re-fi loan will dramatically lower your interest rate, allowing you to shorten the loan term and pay off the car quicker.
Getting a re-fi car loan in your name only takes mom off the deal and reduces her liability. In a few years if you decide to trade in the Dart, you will have a solid credit history with a highly regarded institution and will probably qualify for a low interest loan.
There are definite benefits to being in the military and I hope you take advantage of everything available to you. Thanks for your service.