In my state, a trade in is taken against the purchase price of the new vehicle. This reduces the taxes on the new vehicle by the value of the trade. I knew I could get more for truck by selling it privately than what the dealer would give me and the tax break I would receive, so I sold it myself.
If you rely on the vehicle as a daily driver and need the money to make a down payment, you really have few options other than to get best trade in value while not paying too much for your new vehicle. Perhaps you should get the best price on your new truck first without a trade and then start discussing what your current truck is worth. Having evaluations from Edmonds, Nada and Kelly showing what the dealer should give and what the dealer should be able to resell the trade will be the best you can do to bring up your truck value.