The only relationship that will be left to save is one where he has very little respect for you.
I'm so sorry, but the way you're dealing with this is actually sabotaging the relationship, not saving it.
I very much doubt that couples counselling is appropriate at this juncture. You might be incredibly fortunate and find a good therapist who understands infidelity, but they are thin on the ground and there are rather more of the 'let's not talk about the OW, let's talk about your relationship' kind, because that's safe and familiar territory, even if the dynamic between the couple was never the main issue.
I also have a vague memory of an earlier thread where you disclosed your children were getting very concerned and scared about their father's attachment to this other family. I think you might be putting your head in the sand about their internal conflicts too.
If you need a physical separation from a partner and he will not grant it, at that point all attempts to rescue the relationship should cease. When this is added to his complete refusal to give up contact with this woman, going to counselling is very inappropriate. It signals that you still want to work on the relationship, despite every request you make being refused.
Every time you insist on a boundary and it gets broken, you diminish yourself by staying around any longer.
I asked you a while back what was stopping you from ending this relationship and ceasing any more efforts at repair. I think you'd find it so much more helpful to see a personal counsellor to wrestle with this issue because as objective observers, so many of us can see the folly in your passivity and how this is actually working against your apparent objectives to save this relationship, come what may. It might not be too late to switch the counselling appointment to a solo consultation and I'd strongly advise that now.
Longer term, I'd be looking at any other options you might have to living separately from him, e.g. a short let somewhere near the children's schools and legal protection for your financial interests in your current home, if owned. This whole situation is a terrible environment for children who have been troubled for months by their father's behaviour and who can now see their parents living separate lives in their home, with all the tension that entails.
Please think very carefully about your chosen course of action. It's likely to be very damaging to you and your children.