From an objective person, it seems that these are some issues -
1. Her disrespect to comply with your request
2. Your desire for her to halt contact with these men
From her stand point, she may feel that her sense of autonomy is being stifled
On your end, you feel that she should not keep contact with them (Now, this becomes the thing with which you have to come to terms with- figuring out what about her keeping in touch with them is upsetting you. You've mentioned that you do not believe that she's being unfaithful. Then, is it an issue of male pride, underlying insecurity, etc. Once you figure out what the trigger is, the two of you can start to deal with the issues.
This problem can be due to lack of communication (either partner not knowing what the other's feelings are and why they feel this way.)