I agree with SerJR, that with his past history it is
hard to say. He's done this before and let you down badly.
But in my gut opinion this time could be a little different. I've followed your posts and it has always seemed to me that when he has broken NC in the past it's because he is weak and frightened to be alone - not so much because he 'loves' the OW anymore. It seems to me like he no longer thinks she's 'the one' but that she's 'the one who might be left to him' if he can't get you back. So when he's most frightened of not getting you back he goes running straight back to her - giving her just enough to keep her hanging on. It is absolutely all about him and not her.
Now that's not the type of man you want in your life going forward either because you will always fear that weakness is still there in him and anytime there's trouble or a down time in the marriage in future he could go 'running' again. But maybe he is beginning to realise this himself now, and realise that he's the only one who can change that now? Not you and not OW? If so, that's a step forward for him.
I'm hoping your IC has your best interests at heart as well as his by agreeing to that session you had, and because as she is his IC too, she is uniquely situated with an insight into you both. So I would expect (and hope) that she would have pulled him up in front of you if she thought he was lying to you again or had NO hope whatsoever, of keeping the promises he is making this time. Now of course, she can't predict if he will stay the course and follow through on his actions either, anymore than any of us can. But if he has had the 'guts' to say everything in front of her, (and she is witness 'presumably' to any 'growth' he's had in therapy with her) maybe it's the start of him acting on that growth.
Also to blow the OW off publicly in front of your boys - well that seems like two things to me. Maybe he really sees her as a public symptom of his own weakness now and she is embarrassing to him now because of it - just following along behind him and showing his sons his continued weakness in allowing it. She may have really de-fogged him completely by doing that because it also showed her as being weak to still be following him around - a public embarrassment in every way, and all round for him - and hardly someone to run to for strength.... and all played out in front of his own sons no less. Maybe he sees it now. I don't know.
Also he's helping you with buying the house he doesn't 'really' want you to have, (because it makes it 'easier' in his opinion for you to not 'come back' to your old house where he lives) ...so maybe this is him starting to grow a backbone again? Starting to realise that it's more than a house address that needs to change to get you to come back to him? Maybe he's becoming prepared to stand on his own two feet, and burn his bridges to risk being alone if he can't get you back - because the knows that change has to be in him - not you, not OW and not the house?
I don't know. Maybe I'm seeing more than there really is, and it would obviously be a work in progress if this is what is happening anyway. Maybe your heart has been too hurt and you have no more chances to give him. You most certainly do not owe him another chance - he's had quite a few already and he kept on letting you down. But I think because of these actions if I were you and I wasn't completely done with him already, it might give me at least pause that this time it could be different. That maybe he does see the problem has always been in him now and that he is the one who has to fix it. I wouldn't jump right back into R with him - he's hurt you too much already to risk that immediately - but I may be inclined to give him a little more time to 'prove' these changes to me (and to himself too) before I actually filed.
Of course you could still do all that whilst going ahead with the divorce too if you wanted to - there's nothing to say that you can't divorce him and still watch his actions too. That, in fact, would be the ultimate test of any changes he says he's made. You could always get back together with him after - if did maintain his changes - and if you wanted to.
Ultimately though, I think it's not so much the action of filing that divorce that is the risk - it's the building up of your hope again whether you file or not. Getting your hopes up is a risk that ultimately has no guarantees - as you know only too well from previous hurts. What is your gut saying?