Is it cheating?

One of my alters goes to work for me. She is this outgoing, empathetic, smart, assertive, and get down to business person. Unlike my usual passive and introvert self. Lately, I have noted that she has been comments from this resident doctor; and she has been flirting with him. He seeks me out on the unit that I am working on just to stop and talk to me, which is disruptive to my work, but my alter doesn't mind. I am already in a happy marriage, I don't need this relationship with this doctor. How do I make this relationship between her and the doctor stop or at least cool down so that they are continue to be nothing more than acquaintances?

unfortunately to the outside world yes if person or alter is married and another person /alter within the same body dated someone else its considered cheating.

but this is also a normal occurrence with people who are DID. if the alter wasnt present nor co conscious at the time of the wedding they may not perceive themselves as being married or in a committed relationship.

You can stop the situation from going any further by letting this person your alter is attracted to know you are married and happily then talk with your treatment provider. they can help you learn more ways to prevent this from happening again.