Okay. Have been through some of this but not to the extent of the school refusing. DD was depressed and anxious and in a vicious circle. It isn't something they can just snap themselves out of or can be snapped out of.
You need to take control here of school and CAMHS/GP. If she attempted suicide there should have been a formal psychiatric assessment. As to see it and insist on an agreed care plan. If it wasn't done ask why not and for a copy of the Trust's protocols. If there's an issue phone up the commissioners and ask what the procedures are. Attempted suicide at 12 sounds like tier 3 and the cigs should be turning relatively quickly. If they aren't email CEO and commissioner, note your daughter is escalating and that you will be disappointed if there is further escalation after x weeks or months in the system after a suicide attempt and no assessment by a psychiatrist.
When she has had some counselling and possibly when some anti-depressant therapy has started she will start to feel better and be able to reflect better about the causes and to identify and explain them to you.
She might just not have settled into this school but needs some proper clinical help to turn it round. She isn't well; you wouldn't drag a child in physical pain to school so don't do it toba child in mental anguish. Persuade, encourage, cajole, yes - force no.
And it isn't your fault MH services for adolescents is in a,worse state than for adults and CAMHS seems to exist so staff can have multidisciplinary tea parties at their convenience rather than provide useful interventions when they are needed.
She needs a psychiatric assessment. Either fight tooth and nail for it or if you can, pay for it. But don't fight your daughter. It's a shocking system.