Kimberley this is why it is good advice to get some separation and breathing space, because seeing the person you love in such turmoil messes with your head and stops you focusing on your own battles. You see, what you are seeing now is not genuine sorrow or contrition, although it might look like it. What you are actually seeing is self-pity and self-absorption.
Hard as it must be to see the wood for the trees at the moment, try to think logically. If this affair ended in October and he'd regretted it and the harm it had done, you would have seen that in his actions and in his words. If in December when he was informed that he was subject to a disciplinary, the enormity of his actions would have hit home then, especially if the affair was done and dusted. There would have been enormous guilt and regret for a) having the affair and b) jeopardising your home.
What did he do instead at that point in December?
He told you what was actually in his head. That his feelings for you had changed and he wasn't sure whether he loved you.
How somebody feels about their actions before they get found out is far more relevant to what they say they feel after.
Right now, he is sorry that work caught him out and he's sorry that you intercepted that letter before him. All his feelings now are for himself and the mess he's made of his life, not yours or the children's.
You didn't do anything to create this, so please stop feeling irrational guilt towards your children.
My advice is to get some space from him now and let the children come home.