The interest rate paid on the first car along with the down payment are important in determining the amount of negative equity you have. Having negative equity can affect your financing on the second car. The dealer may have to use a bank that is willing to take on the additional risk of negative equity since the car is not worth the loan. You will pay more for the risk level. You're naive if you don't understand that.
You and the dealer are $4,000 apart from a deal and thats more than can be bridged in this deal. Walk away and go to another dealer. I think you'll find that the 4k you're looking for isn't going to happen particularly if you intend to bad mouth them instead of negotiating. I don't think you'll get everything you asked for. If I were the dealer, I'd cut my losses and accept your business as lost.