Back at Ivy's apartment, she tried to convince Harley that she didn't need to prove herself to anyone, but Harley now insisted on joining the Legion of Doom herself.
The Joker then used his own explosive to drop studio equipment on Batman, at which point he kidnapped Robin and fled, forcing Batman to chase after him and abandon Harley and Ivy.
Related: If there's any doubt that the two went there to get married, just zoom in on their hands and you'll find that the two are sporting matching wedding rings.