the basis of my appeal is that my child was very distraught at the time of the entrance exams due to the loss of both grandparents in a few months.
Unfortunately the loss of grandparents tends to come up at appeals quite frequently, and can lack conviction. It will help considerably if there is clear evidence from the school of her distress around the time of the test, and perhaps that there was a marked dip in her academic performance.
I have also submitted references to her academic ability.
This is where the centre of your appeal should be - proving as far as possible that the test result was not representative of her ability.
The school statement says that they are sympathetic to the family situation but there are no concessions for family circumstances.
This is very much a standard statement against oversubscription and you can pretty well ignore it. Focus on the academic evidence instead.