Complex negotiations are often designed to distract you from important issues like trade value and auto loan interest rates. Insist on discussing one issue at a time. Don't be bullied. If you don't understand something, keep asking until you get a clear answer. Knowing what the dealer actually paid allows you to make an offer below their cost and force them into a realistic negotiation.
Manufacturers sometimes offer unadvertised rebates to their dealers.
You may never know about these unless you make that low offer. Negotiate hard and keep your offers below cost until you are sure you have seen the best offer. Don't be pushed into an impulse decision. If, after a reasonable period of time, things don't move quickly enough, force the issue by making a show of your intent to leave. Be convincing, experienced salespeople have seen it all.