Hi, I'd like to help you with your question.
Your sister in law's husband does not have a sexual addiction, unless he is hiding a good portion of his extramarital behavior. Sexual addiction does not involve one person, it involved multiple partners with little to no emotional connection to those partners. Addiction involves the need for sex with no thought to a relationship.
Your sister in law's husband, however, has a relationship with this former co worker and is not willing to give it up, even to save his marriage. If your sister in law has given him three chances to stop seeing this other woman and he still will not, then he has no intention of doing so until he decides to stop.
Your sister in law can insist he stop and insist on counseling. But the desire to discontinue the relationship and repair the marriage must come from him. And so far, he is saying he is remorseful but his actions say he is not. No one is going to change unless they want to change and so far he is not interested in changing.
In cases like this, it sometimes takes a separation to startle the cheating spouse into acknowledging there is a problem. Your sister in law may want to let her husband know that he needs to leave the family home and only contact her when he is ready to stop having affairs. Then follow through. No more chances. When he sees she is serious, he may stop his extramarital behavior.
Here are some resources to help your sister in law:
I hope this has helped,