Joining a league formed against her wishes that competes with her league in terms of name recognition, undermining her efforts to create a cohesive team and have some modicum of authority in the superhero community.
Hal's league is kind of a slap in the face to Dinah, basically saying she, the JLA Chair, doesn't deserve his respect--he doesn't have to listen to her. This makes her life a whole lot harder, since now her team is one of two options rather than the definitive JLA. Now she has to explain to new recruits why her team is better, rather than relying on the fact that it's the Goddamn Justice League. Not only that, but she now lacks the support of her friend, Hal, her husband, Ollie, and the rest of Hal's team. They may not be directly obstructing her efforts or working in direct opposition to her goals, but they are basically abandoning her when she most needs help asserting her authority.
This is a big problem that women often have to face when they come into power. Sensible men who generally respect women and would be terribly offended if you suggested they didn't often having a hard time taking a female leader as seriously as they should. Dinah is the Justice League chair, whether Hal likes it or not, and if he doesn't like it he can refuse to take part. But assuming he has the same amount of authority because he's also founding member is not okay. Maybe he would've done the same to J'onn, Bruce, or Clark, but he didn't. He did it to Dinah, who has the least amount of weight out of the founding members and thus needs his support more. And because she was the Chair, she did have that much more authority than he did.
If it was just an ordinary team and not another League, I'd have no problem with Ollie joining it. However, the public of the DCU are going to view it as Hal's League vs. Dinah's League, regardless of how the leagues themselves present it. That's how people work. Ollie shouldn't be taking Hal's side in this, and as a media-savvy politician, he should know how it'd look. Considering who he is, it looks like he's made the deliberate choice to side with Hal over Dinah, and I'm really not okay with that.