My experience has been that it's really tough to sell a vehicle once you hit a certain price point where the typical buyer needs financing, and the typical buyer can't or won't go the extra mile to get a loan on a FSBO vehicle. I would definitely trade it in, or sell it to another dealer. That said, I would bargain hard on both ends of the deal, and not overpay for a replacement car because the trade value is clouding the deal.
I would do the following. IF you have enough cash, find the car you want and buy it. Dealers make money on financing, so they are often less than impressed that you have cash. However a straight cash deal for the car you want keeps the trade from muddying the water here. Now take the Toyota to the car buyers at every place you can find in town. Get a firm number from everybody and see who will make the best bid. If the Kia is still in play, your trade offers can be used two ways. First, you can ask the dealer to match your high offer. If they refuse, then ask them to do a "pass through" trade. This is a process where they are rolling the trade over to the high bidder that you found. This is uncommon, but I have done it twice, an it made me a ton of money. It's really a good technique if you live in a state with high sales taxes, since it wipes out the tax burden.
In one case I bought a fully loaded Suburban from a VERY high end luxury/exotic dealer. I paid a little over half what it was worth, since they were horrified to have it on their lot, and just wanted auction value for it. The problem was that they lowballed my trade by about $7K. I had a much better offer from a dealer in another state who specialized in my trade (diesel pick-ups). I actually delivered my trade to a dealer five hours away and shuttled the cashiers check and title back and forth. In the end I came out about $16K ahead on that one. In another case a dealer took a pickup of mine and did a pass through on the purchase of a motorhome, and saved me $1800 in sales tax. By the time I handed him the keys he had flipped it to a local Chevy dealer. Good luck and don't forget that the only way to come out on top is to think about this transaction exactly the opposite way that the dealer wants you to. That being that you are doing two completely separate things here, selling an SUV and buying a small car. Since I appears that you have no sales tax, there is no compelling reason that both deals have to be done at once, or with the same dealer.