Trading in a vehicle that is upside down is not a good idea. All it does is move the negative equity over to the new vehicle loan plus adds additional negative equity from the purchase so you end up in a worse position than you are in right now. You might end up with a better interest rate in a trade, but owe a whole lot more. 
Trading vehicles makes the problem worse, unless you bring enough cash to the trade to pay off the negative equity plus pay down the amount on the new vehicle.
Your idea of refinancing your current vehicle is a better solution. You may have to pay down part or all of the balance of your current loan that is underwater now.
Check with a couple of CU's in your area to see how much they will financing/refinance on your existing vehicle before you pay down your current balance. That way you can get a much lower rate, get rid of most if not all of the negative equity and build another tradeline with a good lender (the CU) all at the same time.
Then, after you have had that loan for at least six months to a year, you can sell your vehicle and get the one you prefer.