I agree with the others here that you may be inadvertently conflating two different things - how you feel about her/your marriage and the nesting issue. In her mind - hence her ‘do what I want it or i’ll file’ - but perhaps in your own.
You are allowed to feel how you feel, but your words of love are obviously not what she wants to hear right now. You’ve said your piece so no need to say it again imho.
On the nesting issue - which if i understand you rightly is that she wants you to buy/rent another place and the two of you take turns using it or being in the house with your kids? Regardless of how you feel, this is not an option you want to take? Why not, out of interest? For reasons that have nothing to do with your feelings for your wife or her opinion? (And don’t get me wrong, I can see a lot of disadvantages to it for you and your kids and few advantages, but some people do choose this option presumably for good reasons….)
But I would encourage you to see these two things as separate….your feelings about how things are vs what you are or are not prepared to do in response to where you are if that makes sense.
You said in an earlier post that she first mentioned this in June. I asked you what your Plan B was when you first said no to it then; you said that you both stayed in the house was your Plan B. It may be that you now need a Plan C, my friend, if your wife is going to turn the pressure up in a very typical MLC way. (Bc they mostly do, particularly in the first year or so, which is why we say it gets worse before it gets better. And often, the thing that gets better is you

)
In addition to that, you can ask her to do or not do certain things for your sake or your kids - how is that working out so far though?

- but you can’t control if she does. And that includes if she files or indeed brings the OM around the kids. That is where boundaries come in….yours with her and your kids with her….if she does x or y, do you know what your boundaries and next steps are.
As I read it, essentially (and in a very MLC way) your wife wants to be ‘free to explore’ a new life with OM while the rest of you shuffle round to make that as easy as possible for her so she doesn’t have to feel too much discomfort about it. That sucks and it’s a s$itty way for a parent to behave imho, but that’s how it is right now. You get to choose though what is acceptable as a way to live for you and your kids given that…..if only on the basis that what is good for three outnumbers what is good for one lol…..and you do have options. She may not like them but that’s not really your primary concern, is it? Everything from her moving out to her own place or with her sister as before or with OM to you doing so to legal separation (depending on where you live) to divorce. Or indeed some blend of these things.
Most of us avoid doing these things at first bc, understandably, we want to see it as a short storm that will pass. In reality, from most of the stories here, it becomes evident that it is more like a hurricane that blew your house down. Your choices are about how or if to make a life in the rubble or pick up your treasures and make a different one.
What is going to be best for you and your kids emotionally, practically and financially?
You can still select that option and love your wife or stand in hope of reconciliation down the line. If you knew for sure that your marriage was over, how and where would you like to live your next chapter? Bc what you can’t do is control her choices or protect her from the pretty predictable consequences of prioritising them over her marriage, home and children. But you can protect your own future life from some of it.
T: 18 M: 12 (at BD) No kids.
H diagnosed with severe depression Oct 15. BD May 16. OW since April 16, maybe earlier. Silent vanisher mostly.
Divorced April 18. XH married ow 6 weeks later.
"Option A is not available so I need to kick the s**t out of Option B" Sheryl Sandberg