yeah that way seems good apart from the fact they give you next to nothing for your car so i feel id be losing out quite a lot doing it that way, would save all the hassle obviously because they would sort it all, but stil, you lose enough on cars as it is i think id feel robbed getting say 5k for it and then paying the rest ontop the cost of my new car.
thats what haggling is for
Never tell the dealer your budget, because if they know you can easily afford a car then they will be less likely to bring the price down