Thats an excellent point - you've got to go forward in life knowing that you are a civilian and not an ex-soldier with something to prove. Don't let yourself become embittered over this, hard as that sounds right now, because it is simply not worth it. You're not the first, you won't be the last and while your mates may be telling you what you want to hear now, your direction and theirs will be taking a different course in future.To the OP.
First off, I'll hold my hand up and say I'm a career civilian, with no experience of Army life. But even I can see from your posts why you might have had problems at Sandhurst. And it's being made pretty clear by far more knowledgeable posters than I that you have zero chance of reversing the decision.
Your future path is now as a civilian and you need to accept that. You have to take a hard, honest look at yourself, realise you were probably removed from Sandhurst for good reason and work on correcting the problems. You also need to start thinking about what civilian career you want and the qualifications you need for success in that. Then you need to crack on and get a job.
You have to stop obsessing about this. Otherwise you'll screw up your civilian career as well as your army one.
It sounds to me like the Army gave you a very fair crack of the whip - you had two attempts at a term, and two sets of CoC to impress and demonstrate that you had potential. That the end of this process resulted in a body of evidence sufficient enough to warrant a discharge SNLR, despite the impact this will have downstream on army manpower plots shows that there was a very serious problem out there.
You have two choices now - you can take the easy route of blaming everyone but yourself and trying to see if there is some kind of conspiracy. You may go down the road of FOIs, grumpy letters to MPs etc in a vain effort to see this reversed. The chances are that you are completely wasting your time and in doing that, will waste a lot of other peoples time too. The paperwork process will be exhaustive and robust, and will set out in great detail why you have been let go. If you do complain or take it further, this will be dug out, sent to the office of whoever replies to your letter and given as cast iron evidence. Bluntly put, no matter how grumpy you feel, you aren't going to change it.
The second option is what I would suggest. Have an honest conversation with yourself - look at the paperwork, and more importantly, get a couple of mates you trust to look at it too, without telling them the situation. Ask them if it reflects what they think of you. Then, work on the weaknesses, try to overcome them by other means and take steps to become a better person.
There is no shame in not passing out of Sandhurst - you did well to pass AOSB, but bluntly the Army is not for everyone, no matter how good they think they are. They don't discharge for shits and giggles, and you and you alone are responsible for the circumstances of your departure. Accept responsibility for what went wrong, learn from it and move on.
I wish you every success in your future as a civilian.