Work out a price first on the new car, THEN inform the dealer of the trade and see what they offer.
Not sure where you are getting this "trade" number from, but in the real world it might be different.
Usually in these cases it's best to sell the car privately. Trades to dealers are done strictly for your convenience---a convenience that you will pay thousands of dollars for.
Of course, if your car is one that's hard to unload right now, then maybe negotiating with the dealer is the way to go. As long as the dealer sees profit in re-selling your car, he'll work a deal.