Amy, I'm sorry to be the one that says this, but I think from what you are saying, the die is cast.
You are saying that you won't take a break from the OM, won't tell H you are having doubts and certainly won't tell him the truth. You don't believe you will ever feel the "right" feelings for your H. You recognise that it is likely that your H will find out about the OM and that it will be much more hurtful if this emerges later on.
You are saying that the counsellor, much to your surprise appears to be saying "go for it". It would be much to my surprise too, if any counsellor implied this in your situation - I wonder whether you are putting your slant on what you are hearing, or whether you have got a rogue counsellor?
You often say that you can't believe you are in this situation - almost as though this is all happening to someone else. I sense you want someone to come along and tell you it will be alright. Which ever way this situation pans out, there will be enormous pain and hurt - you yourself think that you will never be happy again, now this has happened. But you can try to limit the damage by making some fair and rational decisions now.
I think when you are in the midst of a situation like this, a sort of paralysis sets in and therefore you will do nothing until someone or something forces your hand. Forced decisions of any kind cause more pain - and often aren't the right ones to make.
If I were your counsellor, I wouldn't judge you, but I would try to get you to face up to the responsibilities you face while trying to balance your right to happiness. I would be asking you to list the real consequences of all this - and trying to get you to project the future.
To me, there are two worst case scenarios here. The first is in my view a bit worse then the other because of the shock it will cause, but they are both bloody awful.
The first is that you continue to deny your husband choices, then get rushed into a decision to leave (either by OM's insistence or when your H finds out). You leave and the children are devastated and torn about who they elect to live alongside. Your DCs hate the OM with a passion and refuse to meet him, out of respect for their Dad. You still believe that love conquers all and try to be happy with OM, but the hurt and recriminations get in the way. You start to resent him for the fall-out and start to notice things in him that you are currently blind to. And of course, he is going through the same thing - a devastated partner and kids and all of the above. Eventually, you realise with some clarity that this isn't how it was supposed to be at all....
The second worst case scenario is that you continue seeing the OM, until one of you gets cold feet and breaks it off. You never tell your H about all this and continue with a relationship that is by now much more lacklustre than it was before the affair. The secret lingers over you and you find it impossible to feel anything approaching intimacy with your H. You secretly resent your H for your predicament and wonder all the time "what if?" You are both unhappy in your own ways and other affairs for both of you are now entirely possible. Your children pick up on the simmering resentment and learn some awful lessons about how adults relate when they are married.....
I think you imagine this is how it might be, perhaps not in all its awfulness - and this is paralysing you. But there is a vast middle ground here you know, Amy. If you do nothing but submit to what you see as inevitable, the above scenarios might well happen - and in all probability you are right, you won't ever be happy.
Going for the middle ground (some honesty with your H, a genuine attempt to cease contact with OM) is difficult now, but it actually gives you and everyone else involved (not least your children) the chance of actually being happy in the future. You will feel that having started this all off with a great wrong, you tried your best to avoid the wrong causing more damage than it needed to. This all requires enormous courage and very adult behaviour - and real clarity about the consequences of metaphorically pulling the duvet over your head and hoping it will go away. I'm the same age as you - and I think we all have a moment in life when we have to tell ourselves: "I'm a grown up now - I've got to take responsibility for my choices."
As you can imagine, there are other equally likely scenarios, but only if you do the right thing now.
It could be that this affair provides the wake-up call that both you and OM needed to revitalise your primary relationships. After some pain and much honesty, you find that you have a much richer relationship with your H and your kids benefit enormously.
Or you try very hard to separate your feelings about OM from those towards your H, but despite being honest with your H that your marriage is in peril, you and he are unable to rescue the relationship and you part. OM has made the same efforts in his own relationship and reaches the same conclusion. You get together and you are happy - sorry that your relationship started by deceiving others, but satisfied that you tried to minimise the hurt and damage as much as you could. Your kids know that you tried your best, because you are honest with them - and tell them what happened and why. Your (now ex) H is hurt that he was ever deceived, but grudgingly admits that he got the chance to win you back and that you tried to rescue the marriage.
I understand that this is terrifying - and I sympathise, but if the die really is cast, then all you can do is to start being honest and understand what those choices might mean - and take full responsibility for them.
FWIW, I don't think you've got anything like enough information about your true feelings for OM in order to make this decision, but I also don't think you've got enough information on your true feelings for your H either. Inertia won't bring you that information though, positive action now is far more likely to achieve that.
I really do wish you well.