Is it best to submit just a letter outlining our reasons and then once this has been acknowledged follow up with the full details and supporting evidence before a hearing?
It doesn't matter - it's entirely up to you.
Also, can an appeal be refused based upon the reason/grounds for appeal or do they have to hear ALL appeals regardless?
No, the appeal must be heard, and you must be invited to attend the hearing.
I know that there are many considering appeals to various GS in Essex but I do feel we have some particularly personal circumstances to back up our case. Any advice or help would be welcome, thank you.
Do bear in mind the importance of academic evidence - which is not to say that your personal circumstances shouldn't be mentioned or wouldn't receive proper consideration.