I know this has died down now, and I actually don't think you've cheated on her. But I'll give you my end of it because the fact you've posted this question in the way you have is rather unnerving. The whole post is based on the premise that she's in the wrong for accusing you of this. But mate, she hasn't just pulled it out of the blue. You've done something to make her think this. Your question is worded so that we all think she's genuinely having a psychotic episode. I'll pick this apart for you, tell me to fuck off if you want, obviously, but I'd imagine her side of this would be similar.

'I ended up losing my temper and told her that this sort of non-communicative behaviour can only jeopardise our relationship, this got her very angry and she screamed at me "how fucking ironic that the cheating husband accuses his wife of jeopardising their relationship"'...

This is saying that you merely lost your temper and then produced a coherant, constructive response, and she totally lost her shit.

'Now I know what a bunch of you are thinking, her attitude is just her projecting her infidelity on me'...Actually, I'm still wondering what exactly it is you've done to her to make her distrust you to this extent. Realistically, YOU HIRED A PRIVATE INVESTIGATOR. As if that's not reason enough to distrust you already. Anyone who's having their wife independently investigated, is not to be trusted themselves.

This whole entire post is built on the premise that she's entirely in the wrong for accusing you of this while you've done absolutely nothing wrong. But you definitely did something mate, I don't think you cheated, but you did something that caused her to distrust you. And your total ignorance to that fact is likely the reason your relationship is breaking down.

You need to change your mindset on it. You don't need to rationalise her behaviour...her behaviour is perfectly rational, she doesn't have to conform to your way of thinking, she can think however she fucking pleases. You need to rationalise your own, and fast. Because you're going to lose her.

I should apologise for the aggression in this but I actually feel the need to defend her in this situation against you. Change your fucking mindset, you don't deserve to be in a loving marriage while you believe that she has to conform to your way of thinking.