Do you have recovery college in Scotland? My DB has paranoid schizophrenia and made the most progress when he went to RC. He also went to a hearing voices support group. It took me a long time to understand but instead of talking him out of the voices etc I learned its better to say 'that must be very scary for you'.
I'm not the thought police after all, DBs free to think what he wants. He's able to recognise it now e.g. he can say I've been having some really loopy thoughts etc.
I think its a pretty unrealistic ask for someone to have full insight after a couple of years - it's like asking someone who had a cancer diagnosis to explain the entirety of what the experience has meant to them. It's not like that. It's an ongoing process of evolving and getting used to how the brain works. It took my DB a few years to settle. He also had a lot of housing changes around then and he was using recreational drugs so probably didn't help.
If you can encourage your DD to groups that might be good, she's quite young and her brain is still developing so anything that safely builds her independence will benefit her in the long run. If she's well enough eventually there's The Kings Trust which works with young people up to 30, they have short Getting Started courses.
Just to give you hope, my DB was dx at 26 and sectioned, he's never been sectioned since and is now 48. He went back once voluntarily for respite years ago. Important to mention that it is possible as the outcomes often seem so bad for schizophrenia. I have always worried about his safety though, only now that I'm trying to train myself out of worrying as much.
I wouldn't get too hung up on the label - I read somewhere they were talking of reclassifying schizophrenia as psychosis spectrum disorder. I don't know that antipsychotic medication has moved on for decades. I think they mostly work by blocking dopamine receptors as the theory is the psychosis is caused by too much dopamine, but they don't work for everyone. Most clinical trials have been done on men in medical research.
But you have to weigh up pros and cons. DB takes the olanzapine as it helps him sleep he says. He got on better with it when he started taking an antidepressant with it as well.
Best of luck.