Emily M. Brown discusses treatment of a split self affair in her book Patterns of infidelity and their treatment (a clinician's version of Affairs: A Guide to Working Through the Repercussions of Infidelity). She states that in this type of affair, it is often the case that both partners are split selves. To the degree that I am also a split self, the treatment for the betraying partner is also relevant to me.
Brown describes the development of the internal dynamic of a split-self on p.56:
Dave...grew up with a mother who was always hurt if Dave didn't do what she wanted him to do. Dave found it easiest to try to please her. When he didn't yield to his mother's neediness and instead did something that mattered to him, he paid for it emotionally with guilt at the hurt he caused his mother. Dave was in a double bind: he could caretake his mother and give up a piece of himself, or he could take care of himself and feel guilty. Dave coped by doing it right (caretaking his mother) most of the time, and hiding those activities that he thought his mother would react to with hurt. It is this kind of bind that underlies the Split Self Affair.
Because the split self is very good at "doing things right," they appear like ideal clients in therapy: hard workers, responsible, low conflict, very rational and likable. But the fact that they remain very rational is the very problem. In order to heal, they must own their emotional self and join it with their rational self. Doing this is near impossible without the assistance of therapy, and Brown goes further to suggest it is long term work, usually requiring several years.
To do this, one must learn to identify their emotions (e.g. through bodily sensations). It can also be helpful to identify and understand how the split formed and became a necessary function. As the client progresses with their ability to identify feelings, the next step is to assist them with being honest - first with themselves and later with others. Most clients will recognize at this point that their dishonesty is troubling and desire to work through it at this stage in therapy.
If the client is able to start being honest with themselves and their feelings, they will find a whole new world of communication suddenly open up, one which did not exist before. They will see the opportunity to actually communicate what they really feel, even in the face of negative responses. It is at this time that the betraying partner may finally be ready to have an honest discussion about the affair with the spouse.
As the split self learns to explore their emotional self, it is not uncommon for them to decide to put their affair on hold. They may also benefit from living alone, which could assist in their emotional exploration and the cessation of co-dependent behaviors. They will have to decide how to spend their time, and it is helpful for them to monitor their choices, feelings, thoughts and the consequences. Some poor choices will probably occur as they learn, however, with assistance, a balance will hopefully be struck between responsibilities and satisfying their emotions and needs.