I think that's a common problem here, conflicting actions.
What does your gut tell you to do?
I would say at home, when you see her, be genuiune and see how her days was. But I wouldn't call and text her a lot and I wouldn't necessarily share with her what I'm doing when out and who I'm doing it with.....
In terms of the OM, I would just let him know that you know about him and don't consider him much of an issue.