How do you convince a spouse that you haven't cheated?

My wife is dead set in believing that I cheated on her since we've been married. The fact of the matter is I haven't. I have put myself in situations that would make it seem like I possibly have. For example, I had a party with people I work with when she was out of town and someone left their bobby pins in my bedroom bathroom in which was being used just as much as our guest bathroom due to the convenience of it being near our back patio. I still to this day have no clue who they belong to and she still continuously accuses me of knowing. I know that's a no brainer that she would be upset but I am completely 100% innocent. How can I convince her otherwise? I have lied to her in the past and I know that contributes to her mistrust. She wants me to take a polygraph test and I am not supposed to because I hold clified information and it isn't legal for a third party to collect information on me regardless of what it is. I am half tempted to just appease her and take the test but then I potentially could harm my career. She doesn't understand that at all. She insists that I am lying. I continue to reure her I am not. I have changed my habits such as I quit drinking and I don't leave my house when she's not home other than to go to the grocery store or go to work. I stayed up late every night while she was away for a few months and talked to her on the phone draining myself of the energy to function normally without some form of energy boost i.e. 5 hour energy drinks. I averaged about 3 to 5 hours of sleep during the work week and stayed up late to talk to her every night on the weekends. We seperated back in September and for the 1st two weeks she was gone we really didn't speak. She thinks i was up to no good then as well but in all honesty I could barely get out of bed or go to work without breaking down. I even pondered seeking psychiatric help to help with my severe depression. Her and I will never be at peace because she won't think differently. There's no budging in her mind that I didn't cheat. I openly admitted to cheating on her before we were married. Could this be contributing to her mistrust along with a handful of lies that I have done in the last couple of years? The last lie that set her over the edge was that I was friends again with a girl who was my best friend for the better part of 4 years. The issue with that was i didn't tell shannyn. I should've but things were going so well with my wife and I that i was afraid to hear her reaction. She found out by looking at my phone record to see that I had spoken with my friend morgan for an hour after I talked to her. Morgan and I had about a 2 and a half year break in our friendship so that hour on the phone honestly consisted of catching up on the two year span of time. I know I am an idiot for not telling shannyn about my friendship but I lie to her in fear of her leaving me. She has threatened divorce on me so many times that I struggled to even tell her anything that I know will cause an argument. Not so much now because I am at a point where no matter what either way if she's going to leave me then at least I can be honest with myself. I know I have rambled on but I am desperate and the only thing I can do to convince her is to give in to her request for a polygraph. I want to wait until at least I am out of the military though but I know she won't be up for it. I love her so much and I literally kiss her *** and do whatever it takes to make her happy and in return I get minimal affection and I feel like sometimes she can't even stand to kiss me or hug me. I don't know what else to do but i want to save my marriage and make her trust me. Do you have any advice?