Do you think borderline fits your daugher?
Cutting & suicide attempts aren't enough to put her in a BPD category alone.
From what I've read & people I've met with borderline, there's usually some type of childhood trauma that starts it and they have a weird kind of separation anxiety where they want to be loved, but they're terrified of being rejected/abandoned, so they can treat the people closest to them very badly one minute & be very loving the next.
And, they people I've known with borderline can be very dramatic. They can also be very charming to people they've just met.
That's what stands out to me the most - reading over a symptom list might help you wrap your mind around it.
BPD is actually harder to treat than SZ from what I understand, so it's not like they're doing her a favor with that diagnosis.
And, I agree with Hereandhere - if the meds work, they work - it doesn't matter what label someone wants use.