I think that by telling her you want to reconcile – basically no matter what – you have removed that fragility from her. She has no need to be careful.
I think that's true, and I think that may be a Good Thing. In committing with no strings, you gave your W permission to be herself.
The problem is that one needs to be ready to cut one's losses if the WS does not act remorsefully. You're not there yet. That's OK ... if you are getting yourself there.
IMO, you need to make D an option for your sake and for the sake of your kids. Many people say they'd rather be from a broken home than in one. D at least frees you to make the most of your own abilities without being bogged down by an excessively dysfunctional spouse.
I need you to convince me that you are never going to cheat on me again, and I need to see you doing things I ask to get me there.
I think you're setting the bar too low. I think what you may be - probably are - setting yourself up for an unhappy life.
You need to work together to define the M that you will build. If you don't come to an agreement on what that M will be, your best bet, IMO, is to split and to be the best co-parents you can be.
There's a difference between 'I'm pretty confident they won't cheat again,' and 'I'm happy to be with them.'
To commit to R, I wanted a remorseful WS, and I also wanted 'yes' answers to 3 questions:
Do you love me?
Are you in love with me? (I didn't realize it yet, but I really meant, 'Do you desire me sexually?')
Will you be monogamous from now on?
I feared the answers to those questions, but I asked them anyway. SI told me I had to risk the M to save it.
What answers do you fear the most? Those are probably the questions you need most to ask.
BTW, IMO 'commitment' to R includes that you'll split if R doesn't go well. That doesn't need to be said - D is ALWYS on the table in an M.
I think maybe she is just trying to communicate what she wants our "new marriage" to be, but it comes across as her criticizing me for everything.
A good MC can help you distinguish between blame-shifting and 'defining a new M.' My guess is that she's blame-shifting, but that's just a guess based on what you've written.
I was mostly complaining about how it would have been much easier to have waited to agree to R in the beginning, and only committed to that after seeing real change from her. She would have seen real consequences early on, and directly in response to her behavior.
The path to healing is through your internal processing, not externals. The shorthand way of saying it is: you need to set and maintain your boundaries.
On d-day, and for some months afterward, it's very difficult to know what one wants their boundaries to be. As others have said, you can change your mind.
*****
You ask a some questions that can be answered only by someone who knows what the future will bring. No one can do that reliably. (The mythical Cassandra could, of course, but nobody believed her.) My reco is to recognize your questions for what they are and to put the ones about the future aside. I suspect they're products of fear.
Fear of the unknown is pretty normal. Just don't let it drive your decision-making. You pretty much have to take risks to heal from being betrayed.