Exam boards will produce modified papers if asked in advance but this is usually about making sure that diagrams are clear for students with visual impairments and things of that nature. I have never heard of exam boards agreeing to remove potentially triggering topics and think it is unlikely they would do this as this would be changing the exam to a different exam altogether.
Where students need exam papers enlarged from A4 to A3 or copied onto coloured paper, permission can be given to open the papers early to allow time to do this. I wonder if this is the way to go. The school could open the paper early and cover up the triggering parts.
This is a very unusual request and it is not possible for the school to apply for this through the normal procedures. Someone will need to have a discussion with the examining boards for all the different exams (schools often use a variety of examining boards for different subjects e.g. AQA, Edexcel, WJEC). The obvious person to have this discussion is the SENCO, though many schools have exams officers as well who may take on this task.
Your EP recommendation is vitally important as will be evidence from school about your daughter's difficulties and what they are doing to meet her needs, known as "normal way of working".
Ultimately, the decision lies with the individual examining boards, not with the school. The school's responsibility is to apply for the adjustment and provide the evidence required.
You are so right to be addressing this now. Because this is an unusual request, you don't want to be having these conversations just before the exams.