I think the coroner would want to see some evidence before calling Tattlelife to attend.
Many Coroners are lawyers and barristers (more often than medical background) so I’d expect a certain level of due diligence. It’s a website, if they can’t even produce some screenshots it’s not going to be taken very seriously that it’s a main contributor. I think due to the SS involvement and possibly family court there might be some restrictions on what is reported.
Generally coroner's officers, who are often police civilian staff, investigate the death on the coroner's behalf. In an average suicide (horrible way to put it but I've seen far too many cases), there would be: witness statements from the person(s) who found the body and from the person(s) who last saw the deceased alive;
Statements from the police officers attending the scene;
Reports from the deceased's GP;
Confirmation of whether the deceased was open to any mental health or addiction services when they died, and reports and records from those services if so;
a post-mortem report written by the pathologist;
a toxicology report giving the results of drug and alcohol tests on the body;
Sometimes a family statement giving a background of the deceased's life (if not already covered in the witness statements)
In a child's suicide, the coroner will also generally request a report from their school or college, and records and a report from any social care involvement (children's services, safeguarding, fostering, etc). On top of that, in any suicide inquest, if the family is insistent that someone or something has influenced the child to take their own life, the coroner may direct her officers that statements should be taken, reports requested and evidence gathered. The coroner will then review the evidence and decide who to call to the inquest hearing to answer questions.
It should be remembered that an inquest is an inquisitorial hearing aimed at determining 'the means by which the deceased came by their death'. A coroner cannot find a person or organisation 'guilty' of causing a death, although they can indicate in their conclusion if they feel something more than minimally contributed to the death.
Inquests are public hearings because, in law, the dead have no right to privacy. However, the coroner can request the press to exercise caution in reporting if there is another minor related to the case who would be readily identifiable (which would be a bit of a nonsense in this case, in my opinion, because both girls are readily identifiable through their mother's actions)