Your integrity has faltered once. If you come clean on that, it can probably be understood and forgiven. But if you try
Can't speak definitively to the impact on your career, but you should tell the truth, if for no other reason, it's the easiest thing to remember. Besides, you never know who or what the interviewer on the other side of the table already knows. The last thing you want is to not tell them and they find out. You''re integrity has already faltered once. If it's perceived as faltering again, I'd imagine your chances of anything other than a regional would be nil, and that's only in the current hiring environment.
The thing I'm curious about is the impact it has had on your military flying career. Does the military vet their instructor candidates before assigning them? I think it's fair to say that it takes a special kind of person to be an effective instructor, and you wouldn't want just anyone doing that. To me it seems you were set up to fail because you were assigned duty you didn't want and may not have been suited for.