Hey Anonymous22, thanks for updating us on what's going on.
What you're going through, the strongly mixed feelings about TPOs/divorce/family unity, are pretty normal for someone in your situation. Of course you want to keep the family together, and are trying different things (TPO, separation, shorter separation, longer separation, coming back to the house...) that you've never had to try before.
The first thing that stood out to me in your update was this:
He told me yesterday that his therapist has said that he should leave me, because I am a lier, cheater, vindictive, etc.
I read this
a lot on the boards, so you are very not alone in experiencing a spouse/partner/ex telling you "this is what the therapist told me" and it's really negative about you and positive about them.
As you step back and have had a day or so to "take a breath" and get some distance from that, what do you think?
Do you think your H is accurately telling you exactly what his T said?
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Another thing I'm noticing is this:
In a weird way, he is kind of being straightforward about what he wants/is going to do.
-He has rented another house.
-He is wanting to be separated for longer than you suggested.
-He says that people are telling him to leave you.
-Pretty much everything you do or don't do "proves" to him that you are "bad".
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I get not wanting your marriage to end or your family to be not unified. Nobody gets married because they want the marriage to end, nobody wants that.
That being said, in this day and age, one partner cannot force or make the other partner stay married.
There are a couple of ways to approach it when one partner is doing and saying things that indicate not wanting to stay married. (I would assess your H as doing and saying things that, whether he "means" it or not, communicate that he doesn't want to be in a healthy marriage right now)
One way is to try to do anything and everything the "less committed" partner wants or says, in hopes that they can be appeased into staying. When the less committed partner is dysfunctional and abusive, this means that the more committed partner might end up trying lots of unhealthy things (pleading, compromising, acquiescing, caving in, agreeing to things that aren't true, etc). Doing unhealthy things isn't helpful for making a marriage healthier and stronger.
Another approach is to focus on becoming a more healthy individual, no matter what the less committed partner says or does. This is often difficult at first, as it'll mean making firmer choices and sticking with them, even if the other partner "throws a tantrum". You have young kids

so I'm sure you know that if a toddler throws a tantrum to get something, the last thing you want to do is "train" the toddler that that's effective. You've probably had times where you had to "outlast" the tantrum, knowing that while it was uncomfortable in the moment, long term it was healthier for both of you.
This is where you seeing a counselor is a great idea. A counselor can help you work through the feelings of fear that your marriage will fail (again, you are not alone in having those fears

), and can be there with you as you figure out what is under your control and what is not. The counselor can also help you stay strong if you start making healthier choices that are uncomfortable and that your H reacts to with "tantrums".
In fact, as I'm typing this, I'm wondering if your H is "tantruming" in a way, by blaming you, "leaving in a huff" to the rental, making demands, etc. What do you think?
In a weird way, working on being a healthier individual first, no matter what the other partner does, is ultimately better for the family members, no matter what happens down the road. All you can control is you. It's hard that you can't make your H want to both stay in the marriage and have it be healthy. What you can try, though, is working on yourself, and you can see if he wants to follow your lead as you model being an emotional leader.
So glad you have a counselor. I think you're making a wise decision to agree to have the counselors talk to each other. Family T is a great idea, too. The more professional support you have now, the better.
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Let's start with that for now. Keep us updated on how you're doing these days... hope the kids' sports are going well

kells76