Sorry to hear you are going through this. I divorced 5 years ago after a 6 year marriage so I feel you.
In reading your posts, my first observation is that you might be giving her a pass on a lot of things based solely on your new found knowledge of MB Personality Types. While I do believe in those personality types, if you boil down men vs women (without personality types), what you are describing of her characteristics and your characteristics aren't unique to personality types - they are simply how 99% of men are and think and how 99% of women are and think. Men = logical and execution. Women = emotional and dreamers. There are various ranges on the scale of each but that's how it is at the core. The classic book Men are from Mars, Women are from Venus is based exactly on this and how to try to understand each other given the differences in thought.
Her living in her dreams and emotions and making decisions based on them is no excuse for the actual decisions she is making. You can't say a woman cheated and it's ok because her personality type makes her X, Y, or Z (for example). At the end of the day, we are ALL responsible for our ACTIONS regardless of which factors in our brains led us to choose those actions. I see you taking a lot of blame here for "not understanding her" but I don't see you holding her accountable for the same exact thing.
When I read some of the things she says (like your example of saying it's beautiful outside and then her responding with a complaint), that has nothing to do with miscommunication in my opinion. That has to do with a person who is upset and frustrated, and they often don't know exactly why, but they take it out on you. From my experience and observation, once a woman paints YOU as the source of her emotional angst (fear, anger, frustration, whatever), the relationship is over and you can't come back from it. What I see time and time again in women like this, is a lack of internal self-fulfillment or recognition of what it is that they want, combined with a permanent sense of wander-lust and dreams about "what could be." These women follow all a pattern and that pattern is one of seeking out fulfillment EXTERNALLY and they always place EXTERNAL factors on their happiness or lack thereof. They get into relationships and think the relationship will be the answer to all their problems. When that doesn't fix their lack of internal fulfillment, they decide they want a pet, or a vacation, or a house, or kids, or whatever. When those things don't fix their lack of internal fulfillment, the process of devaluing you and your relationship is what comes next. Now YOU are the source of their frustration and they begin saying the types of things she has been saying to you, and after a period of time (which usually lasts longer if you have kids binding you together), their repeated thought-process of blaming you for their unhappiness becomes deeply rooted in their mind and it is VERY difficult to undo at that point. Instead they spend their time fantasizing and day-dreaming about how much better their life would be if they could get away, and see friends and start dating again, and find that perfect man that's going to be the solution to their internal problems that you weren't able to fix for them (even if they won't admit it to you that this is what they have planned).
Then they move out and move on and fade away while they seek out what they think will be the answer to their lack of fulfillment. Usually when they get a new boyfriend, it starts really strong but then the exact same cycle repeats itself and they move on to the next thing. These types of people simply aren't capable of sustained relationships due to the lack of understanding and acceptance that their unhappiness comes from within, and if they get that far, then they have to be willing and able to put forth the self-improvement work (through therapy, reading, workshops, whatever), to resolve that for themselves. That is a BIG undertaking, and as you have seen in therapy, it requires a seriously good therapist to try to ask them the right questions to get them to realize and see their own internal motivations and problems - and then they have to be WILLING to accept them too. For many people, the dream reality in their minds about the way things are is more important and powerful than reality. Reality can be a drag, after all....
If I were in your shoes, I would be taking steps immediately to detach from this relationship and assume you are looking at a future that doesn't involve her other than co-parenting. You can't fix her wanderlust (no man can) and unless the therapy sessions are so good that she has an epiphany and a break-through, the chances of her wanting to get back with you are slim to none. She has likely made her decision a long time ago but has delayed acting on it because of the kids. For her to finally get to the point where she is pulling the trigger on moving out is a very bad sign and you have to remember that her decision was made long ago so her opinion of you and the relationship has been festering worse and worse ever since. Her mind is made up and going to therapy is likely only something she is doing to try to make it appear that she still actually cares about your relationship (possibly due to guilt about breaking up the home for your children) and over time, the distance will grow and things will continue to unwind. Even her saying she still wants to work it out is likely a farce.
So again, I would detach, make myself scarce, quit communicating about anything other than logistics and children, slow up the responses, don't ask her about her life and what's going on with her friends or her new apartment, etc, and if you really want to, continue going to therapy with her and do make an effort with that just in case the therapist can make something click for her but I wouldn't hold out a lot of hope. This has been a long time coming for her and would be really hard to come back from. I really don't like giving you this message because I know how difficult it is to hear, but this is my opinion based on multiple LTRs with these kinds of women, including one marriage.