I think there's been a pattern for a long time of you doing things that you don't really feel that great about, or not doing things that are important to you, because either he pushes back at you and wears you down, or because you're afraid that if you stand your ground he will run back to OW.
If you have to make yourself small, dishonest and resentful in order to keep him, it isn't a marriage.
I also want to push back on you not being able to piece until and unless you know, 100% he is over AP. That isn't possible. You are never going to know that. You can look at his behaviour and his words (and like you, I wouldn't be happy with what I was hearing right now) and you can look inside and see if you can trust him or not. But it will always be an act of trust. You can ask for concrete actions - like transparency with his devices, and signing the post-nup - and his eager acceptance of that will go a long way to help, but it won't do the job. You will never ever get past this without having to trust his heart, and I understand why that isn't possible for you right now.
Have you told him that you will live with him and do some friendly co-parenting with the kids, but you are not yet ready to reconcile as his wife because you need more time? I think he thinks you're in piecing. There's so much murkiness here. And I also think you're afraid to be straight with him because if you said, 'I am not ready to work on a reconciliation with you because I don't trust you enough yet' then you think he's going to stop trying and run back to AP.
Maybe it would help to separate the two tasks ahead of you. One is your own healing and recovery and moving past his OW. That you have to do for your own sanity and health and happiness - and it might include forgiveness - whether you stay married or not. You don't need anything from him - he could go off and get married to OW and it is still possible and essential that you do this work.
The other task is your marriage. You have a right there to set boundaries and ask for some non-negotiables from him. But I don't think anything he does or doesn't do in your marriage is going to help you heal.
My IC explained it to me like this - there's you, who needs healing, there's him, that needs healing. You aren't his job, and he's not your job. Then there's the third thing, the marriage, and that needs enthusiastic work from two healthy (or reasonably healthy but also human!) people who agree most of the time on what the work should be and what the marriage is going to look like.
I think he's expecting you to do his work and you're still expecting him to do your work and you're nowhere near working on the marriage yet, but there's no clarity on that between you because you're still very emeshed and too afraid to let go of the dead broken marriage, be single (even if you live together) for a while and work on yourselves.