I can share a similar experience with you. IME, it's good to have one where you understand what the goals are, how the approach is going to achieve said goals, and one that will coordinate with any other IC involved to have an understanding of what is happening with both parties.
Things are much better now since we started seeing a different counselor. Shortly after I discovered affair (but before SAWH admitted to it) we began to see MC that really helped a friend and her husband. Infidelity was not their issue, but I was hopeful this MC (a guy) could help. Obviously, we were in crisis at that point, not only because of infidelity but also MANY years of resentment, poor communication, financial issues, etc. We continued to see this guy individually and as a couple for at least 8 weeks but both of us felt like we were not getting anywhere. I could tell my SAWH did not respect him, for one thing, and we kept having the same argument on an infinite loop every time we were in there. The MC just listened rather than offered advice on how to restructure argument or break it down into pieces or whatever. Also, not having sex was a big issue for me. Here was my SAWH who had been having 'porno' sex with the AP for 2+ years and we had not had sex since way before the affair ever started and he was not interested in moving that process forward. No examination of that was ever discussed in more than 8 sessions with the first MC. During this time, my husband also started seeing an IC and that started peeling back the layers a bit as well.
So after both of us agreed we needed to switch to someone new, we made an appointment with a MC in the same office building but she had different areas of expertise, one of them being sexual dysfunction. We had appointment talked with her and about how things would proceed, what her approach would be, etc. We ended therapeutic relationship with MC#1 and started with MC#2. She gave us an assessment test to see where we were in our marriage as far as compatibility on certain issues such as - being social, alcohol/drug use, religion, child discipline, money issues. THAT WAS EYE OPENING. Even though you know there are problems, that really makes it apparent. You score one way and your spouse scores completely opposite. Yep that explains a lot. The test is one that is offered to people in pre-marital counseling. We just took it a decade too late, apparently. And obviously, if you are in crisis, you are at odds on certain areas of your marriage because you are constantly on the offense (or defense).
Also, in the first few weeks with the MC#2, she saw us individually and as a couple. I feel like she used this time to size both of us up, talk about family of origin issues, etc. It was around this time she began suggesting/hinting to me that I should consider that my husband had sex addiction issue. I had asked my husband this when he started seeing his IC several weeks earlier. He of course said that the IC did not say anything was "wrong" with him. Well, I asked him again during a long weekend drive where just the two of us were in the car. Once again, there had been nothing physical between us and I told him that he is going to have to shit or get off of the pot so to speak at some point because I am not staying in a marriage like this, don't want to be in a marriage where I am not wanted, etc. Finally standing up for myself after all of these years. And I asked him if he was SA. He said he thinks yes and he needs to go talk with someone about it. So the next day we were with our regularly scheduled MC#2 appointment and she referred him to SA counselor.
Some of the other things she has done that have been productive is that she challenges BOTH of us on our "stuff." I may not have had an affair but I have contributed to breakdown in communication by accepting this kind of treatment by my husband. She's helped me deal with my anger about all of this and made me see that I have the choice to continue to be angry or let go of it (which does not mean I am "ok" with my husband having an affair). Another thing she has done has been to point out that my husband's IC may not be very professional in the sense that he is unwilling to speak with her in the context of the goals of my husband's treatment as it relates to the issues we are working on in MC (lying, his addiction, his control issues, his resentment from childhood, his lack of good role modeling from his parents, attachment issues, etc.). She also keeps tabs on what is going on with his SA counselor. And when there are things that have come up with my husband such as his reluctance to start attending SA meetings, the MC states that it should be his "goal" to do it by "X" date and gets him to commit to doing.
I hope this is helpful to you as you re-enter MC.