After the scene where Harley farts in the Batmobile and leaves to use the bathroom, Nightwing says he'd give Batman 10 dollars to drive away and not look back. He obviously refuses, not just because of the mission, but also because Batman's alter ego, Bruce Wayne, is rich. Ten dollars is pretty much chump change for him.
Given Nightwing has long since left the nest, he's probably relying on his own income to support himself and his crimefighting resources. $10 would be pretty generous for him.
More likely: He's kidding. It's not like Nightwing thought that *any* amount would make Batman consider leaving.
This whole movie is being told from Harley Quinn’s POV! As one would expect, Quinn is an unreliable narrator who wants to make herself the center of the story, which explains the bizarre comedic tone of the film and the OOC moments for Batman and Nightwing, such as Swamp Thing letting Floronic Man go ahead with his plan, leading Batman and Nightwing to set him on fire.
At first, it might seem quite strange that Harley's Puppy-Dog Eyes and Crocodile Tears worked so well on Ivy when she was so set on her plan. But remember: Harley is a fully trained psychologist. She's an expert at identifying and using people's mental weak points, so she knew that if the crying didn't convince Ivy to abandon the plan, nothing would. Her "Works every time." line afterwards proves that she's used this tactic against Ivy before.
While Harley's attempts to reestablish herself in psychiatry failed due to her past as a super villain, there are reasons for people not to want to hire her besides that. The entire reason she became a villain was because she allowed herself to be taken in by her patient's charm, fall under his influence, and be convinced to do illegal things for him. Even if Harley hadn't become a villain, and her only crime had been helping Joker escape, she still would've been fired and blacklisted. Not only for helping an insane mass murderer escape incarceration, but also because she'd shown herself to be susceptible to being manipulated by her patients. A quality you would not want to have in a therapist, even one who wasn't working with criminals.
In the game show Harley hosts at the end, she mentions that people who complete the obstacle course get a year of free therapy with a licensed therapist. While this is nice and all, you have to wonder about all the people (including the poor contestant, who has a really messed up life but fails the course) who lose, are they just SOL and go crazy?
Well, there are other ways to get therapy cheap. The poor contestant could, for example, be treated by a student studying to be a therapist (and supervised by their licensed teachers).
