Right. This is the simplest website that I can find that explains in a straightforward but non-jargon way about what must happen in a gross misconduct case.
http://www.iambeingfired.co.uk/misconduct.html
I suggest that you work your way through it and see that the company has followed the various steps.
In my opinion the business about the emails is a red-herring in the overall assessment of whether your dismissal was fair or not. I can understand why you think it is not, and on the basis of what you have said your boss should not have done those things. However that was not the reason given by the company for your dismissal.
So if you are trying to get your job back, you need to focus on the REASONS GIVEN BY THE COMPANY for your dismissal.
You still haven't told us much them. What is it that you do? If safety is a paramount part of what you supervise and you walked off the job then it could be fair dismissal - I only have small snippets of your story to go on. Much would depend on the extent to which you tried to contact your manager or others, the nature of the emergency at home, what other alternatives you had in those circumstances. I'm afraid that I cannot second guess what the company said to you about the circumstances or its reasons behind its decision.
Then someone independent of the first decision should be reviewing the evidence and the process - that is what the appeal should have been about. I am very surprised that they cannot make a quick decision after 18 December. However you cannot use this delay to enhance your argument that it was unfair (originally).