Gary,
You of course know her better than any of us. Part of her distrust may be born of insecurity, perhaps a previous failed relationship? I'd have a talk with her, something like:
I'm really saddened. I know for a relationship to last, it must have a solid foundation of both love and trust. When a man cheats on his wife (partner), no question that has a devastating and lasting effect on the very foundation of their relationship (or marriage). I want you to know that I value what we have together far too much to ever do that to you. It's not in my nature, not who I am. I believe in you, love and trust you, and hope you still feel the same about me. Sharing a loving trust in each other is the proof of that commitment. I want to always be there for you, and right now I need you more than ever.
Yeah, mushy, but "they" like that that sort of stuff . . . and of course you *do* have to mean it! Going on 45 years, have never so much as lied to her (haven't always told her "everything") but have never cheated or lied.
BTW, if she doesn't truly believe in and trust you, sadly, you really are better off parting ways, 'cause that lack of trust and insecurity on her part will likely remain and come back to visit you again.
bumper