Grace, don't forget that God's plan is bigger than yours and H's too.
Maybe God knows that H is not going to come home and he has something bigger planned for you.
Maybe he has a plan to bring your H home that can only work if your H buys a house with OW and the whole thing with her crashes and burns. (Which it obviously will, whether it's now or years from now or somewhere in between, and whether or not you take him back.)
Your thoughts are not His thoughts.
It's ultimately not about uncertainty, but about the certainty that God's plan is what is best for you. I heard a sermon once about how we are sheep to the shepherd not because we are fluffy and cute and nature-wise but because we are to be that stupid as far as what is best for us! The average sheep will walk off a cliff if the shepherd leads him there. God wants us to be totally free of strategy and plan and "big picture." Just to keep walking and trusting him to guide our steps.
Instead of constantly looking for His will, to realize IT'S ALL HIS WILL. If we step outside his will, he'll call us back. If we won't listen, he'll use our mistakes to realize His will anyway.
I get what you are thinking/doing/feeling as far as doubts and feeling that you are tired of it. We are in a similar place though I have been at it much longer.
I think either you think H is in MLC and don't believe anything he says/does, or you take what he says/does at face value. You seem to be straddling the fence as far as that goes.
I am unclear as to why you are taking on the job of telling your kids about the OW in that way. Why don't you leave that for him to do? I mean, if they ask you about it, tell the truth. Or if it comes up with them, something that would cause you to lie if you didn't tell the truth about her, then say it simply and freely. Otherwise, why are you doing H's dirty work for him?
I believe I will see the bounty of the Lord in the land of the living. Wait for the Lord with courage. Be stouthearted, and wait for the Lord.