Answer: Even though what you badly need is a talented counselor, I'm going to venture an answer to get you out of your lie:
"Why do you think they'd think that?" There can't be even a whiff of accusation or sarcasm to this, or else the whole effort is a goner - the "whole effort" being to open the topic to an actual conversation, instead of her fishing and your lying.
If she answers defensively, ("If," ha, I crack myself up), then go into just-the-facts mode: "I'm not attacking, it's an honest question. You make that remark a lot, and I want to know what you're feeling."
Because feelings are everything here - both what she's feeling (but neither telling you nor acting on in a loving or productive way), and what you're feeling (but neither telling her nor acting on in a loving or productive way). She's acting out, and there's a "why" there that you both need to face.
If you're not sure you can go into a conversation like this without getting angry, snarky, accusatory, defensive, etc., then think carefully about what you'd need to get to that state. Given how high her defenses are, Zen must be your target resting state throughout the discussion. Seriously. She's going to need to feel safe, if that's even possible.
And if not, then please see "counseling," above, but go alone. Control issues and joint counseling don't mix, at least not till individual counseling has progressed to a certain point. Otherwise the controlling half of the couple can manipulate the therapist, which doesn't just erase the value of the treatment, but in fact can make things worse. Plus, controlling people scare their mates out of telling the truth - reread your letter as Exhibit A - and counseling without truth is pointless.
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