If your car is worth trade in $25k and you owe $20k the dealer will give you $5k towards your next car. They don't "take over" payments try simply pay off your loan and then try to sell your car or auction it.
The best thing to do would be to sell it privately, as I did a similar thing due to a circumstance just like yours. It took me 2 months but I sold it and made $6k more then what the dealerships were offering me.
Depending on your current rate refinancing rates are 2.5% and above so unless your current rate is less then that you would be saving money with less of a payment. Good luck, I was fortunate to drive my car for 9 months put 5k miles on it and sell it at only a $500 loss.