Oh my god.
No, I think that's a disingenuous reading of the text, because Garnet tells us why she escaped her mother: Because she doesn't believe she can get through to her, but she believes that Cid might, because they clearly are or used to be old friends and he is a fellow ruler. "Escaping her mother" was never her long-term goal! She loves her mother, she just thinks she's going through a bad phase and needs to be helped.
So her initial goal was "go meet Cid, then come back with him to talk to her mom." But then, Cid decided to send the air fleet to Burmecia. That means he's probably going to stay put for now, not visit Alexandria, since he has to oversee a military action on his frontier. So Dagger is going to have to just stay put while other people address the Burmecia attack, and by the time this unfolds, war might have broken out, and it'll be too late for her to do anything. But as we saw, nobody was willing to let her make her case and listen to her, so she had to take action on her own initiative.
I think under that perspective it makes a certain kind of sense for Dagger to decide to head out on her own against everyone's advice. It's reckless, yes, but, well; she's sixteen.