Ah, it can be a difficult age. A lot of people struggle to own up and become responsible (but I hope your cousin does). It's hard (perhaps even harder than growing up) to say no to these people sometimes. Precisely because they're close to us and we love them, but in the end, I think you did the right thing. I reckon she's gonna learn a lot more from this experience and it will ultimately be more helpful than if you'd allowed her to crash for another 3 months. So stay strong :) She'll thank you for it someday. Hopefully. And even if not, you know you did all you could.
Knowing this, I am satisfied and I feel a lot freer. It wasn't easy saying NO to her but I had to. I just hope she is making the right decisions out there—these are my thoughts because I care about her and I need her to grow up and take responsibility for life. She is going to learn the hard way.