The CAFCASS website has some really good explanations of the process which it's worth your DSis looking at.
I've had experience of several court cases in which one parent applied to court, and each has gone something like this:
In advance of the first hearing - CAFCASS do a preliminary records check of the DCs named in the application; police, SS etc, and write a brief summary for court.
On the day of the first hearing - parents are given a copy of the CAFCASS summary (it should be sent to parents in advance, but never has been in my experience) and each meet with the CAFCASS officer. Solicitors/barristers for each party (if they have them) negotiate to try and reach an agreement.
First hearing - court listens to applicants request and respondents reply. The court may order further reports from CAFCASS, they may order that the parties attempt mediation, attend parenting programme or request other reports they think are necessary . They may make an order for some contact, direct or indirect, while those reports are being written.
Weeks later, Further hearing(s) take place for the court to consider the findings of the reports they have asked for, and for either side to argue their case in more detail before a decision is made.
Once an application has been made to court, only the court can dismiss it - the applicant cannot decide to withdraw it. Even if the applicant doesn't turn up, there will still be a need for the respondent to go into the court room and often, the case is rescheduled at least once, rather than dismissed.