Be happy to be dealing with the good cop.
Implicitly call out the buyer for using this tactic.
Explicitly call out the buyer for using this tactic.
Do a deal so as to avoid having to negotiate with the bad cop.
Ask to work with a different negotiator.
You don’t want to let the other side start by making a threat and having you accede. At the same time, you don’t want to to chill the negotiations by explicitly calling the other side out for using this tactic. Thus the implicit call out is best. This is a great time to use humor—“You’re lucky my spouse isn’t here.”