When a BS asks for space they really need to process what has happened. It isn't an automatic sign that you guys will divorce. The separation is a sign of how deeply infidelity hurt the relationship.
You are seeking IC, which is a very good step. I caution you to find an IC who is familiar with infidelity as a traumatic event akin to surviving a natural disaster, or major accident. The reason is that therapists pretty much split into two camps on infidelity.
Camp 1 is the forgive, forget, move on. This is nothing more than rugsweeping. The therapist looks at the relationship as the source of the infidelity and focuses on that. Problem is that the relationship was never the source of it.
Camp 2 is the therapist group who looks at it as a traumatic event, which recognizes that the wayward made the choices to have the affair and to hide the truth. This path is the longer path which focuses on the wayward internal mental state and works to find out those things deeply inside them which allows or allowed them to make this destructive choice (we call these the why's)
If your relationship is going to heal making you BS feel safe and secure must become the priority in your focus. Betrayed spouses who don't feel safe and secure are hard pressed to move out of the hyper-vigilant early stages of processing the affair. This stage is a normal stage for them because it is at this time they are trying to figure out just what the fuck happened to them and the relationship. It is akin to a veteran who keeps his gun under his pillow after he/she gets back from traumatic tour of duty. That weapon represents safety and security to them.
In much the same way early recovery from infidelity has several things that are like this. The looking at FB pages, phone records, searching the physical phone, looking at computers. These give a small amount of control to the BS which is needed after the world they thought they lived in has been torn apart.
There are several books that I recommend for wayward spouses that can help them to become safe and secure partners.
How to Help Your Spouse Heal From Your Affair: A Compact Manual for the Unfaithful by Linda J. McDonald
Yourhttps://www.amazon.com/HelpSpouse-Heal-Affair/dp/145055332X
PDF found here: https://www.scribd.com/doc/65498163/How-to-Help-11-06-10-Final-PDF
She lists 15 points of action and attitude that the wayward must embrace to build an environment where the betrayed feels safe and secure. Since the initial trust, safety and security are gone, these actions are needed in order to show the betrayed that the wayward partner is doing everything in their power to show they are willing to make you feel safe and secure. These 15 actions and attitudes are:
Waywards who want to rebuild the relationship after an affair
are non defensive
examine their motives for their affairs, without blaming their spouses
accept their roles as healers to their wounded partners
do not resist breaking off all contact with the affair partner
show genuine contrition and remorse for what they have done
make amends and apologize to loved ones
apologize often, especially the first two years
listen with patience and validate their spouses’ pain
allow their spouses a lot of room to express their feelings
respect the betrayed spouse’s timetable for recovering
seek to assure spouses of their love and commitment to fidelity
keep no secrets
do not maintain close ties with those who condoned the affair
are willing to be extremely accountable for their time and activities
frequently check in with spouses as to how they are doing
are aware of and anticipate triggers of the affair
are willing to get rid of hurtful reminders of the affair
don’t minimize the damage the affair had on the children
commit themselves to a long-term plan for recovery, honesty, and Internal (psychological) growth.
The last point includes these actions: (I added these from my own experience)
• Individual counseling for the wayward so they can find out what is inside them that allowed them to rationalize the affair.
• Learning what constitutes safe boundaries in interpersonal relationship.
• Couples counseling once the wayward finds those whys and begins addressing them, and acceptance 100% of the affair is on the wayward (no blame shifting)
• If substance abuse is present then wayward must enter a recovery program in order to get the addiction under control.
The second book is Not Just Friends: Rebuilding Trust and Recovering Your Sanity After Infidelity by Dr. Shirley Glass PhD. This book is one of the best on detailing the recovery process that is needed for a person to deal with the trauma of infidelity. The biggest thing for me in the book was to reanalyze my interpersonal boundaries with people outside my relationship.
Finally have to own your affair 100%. You made the decision to have the affair, your BS didn't force you into it. Your marriage issues didn't make you have an affair. The AP didn't seduce you into it. You have to let go of all ideas that somehow there is someone else to blame for your actions.
McDonald's book is the actions book. Those actions show the BS you are serious about healing the relationship. However Glass' book is the book that shows how the paths to affairs happen. These areas are shitty boundaries, opening up to the AP and closing off the spouse. Glass' book gives a roadmap to healing which includes talking about the affair and bringing it up as the WS.
I would also highly suggest that in your IC you look into Family of Origin issues (FOO) this was one of the biggest areas which I avoided for most of my life. My FOO issues didn't make me choose an affair, but it gave me the tools that made that choice a hell of a lot easier to make.
Even if your BS decides to end your relationship, I urge you to do all of the above. We wayward have something inside of us that allows us to choose to go outside of our marriages and long term relationships to fill something inside of us. Moving down the road without doing this work means that you will still have all the old tools and mental twists and puts any future relationship in danger.
Hang in there.