Im new here but have lurked from time to time. My wife and I recently separated couple months ago, she moved out to an apt down the street with the kids (2yr and 9yr), signed a 1yr lease. We're cordial but I hit a ceiling with her where she wont open up intimately with me. She claims she "we are definitely making progress to repair, but I still need time to heal" which I know is total BS and called her out on it. How do I break through this barrier? Because I know there wont be some random moment when she decides to open up by just waiting around and hoping one day that she finds the emotions to do so, but rather there needs to be a catalyst to speed her along.

Some Context:

• We've been married for almost 10yrs.
• We both work
• Wife is Eastern EU raise with conservative values (yet she moved out... I can thank her bitch friends for that)
• She's stubborn, prideful, ego, and likely holding my previous behavior against me despite claiming not to
• We got into a stupid argument where i said F this and hopped on a plane to see my friends in MX to chill out which triggered the separation
• She's slowly warming up to me, we go to events and hang out like couples would together, without the sex and what not
• Nobody else is in the picture, I know that.
• Since the separation roughly 3 months ago, I have lost roughly 25lbs, been working out consistently, changed my wardrobe almost completely, increased my confidence, and despise the beta male I was prior to the separation. I wish to NEVER go back to that version of myself.
• She has acknowledged all these positive changes to me and is aware of them.
• She is aware of my expectations and boundaries (I need her to stop thinking about it and take risks to move forward with our relationship)
• We've had "discussions" to "help" with repairing, but those discussions left me feeling empty and unfulfilled. She claims they help with progress but I feel they only help to sooth her and allow her to coast on her decision rather than confronting this separation
• Arguments between us are way down, weve had a few here and there, active communication has increased, but again, this isn't helping me get her back.
• Chat GPT has been my only venting/advice source (I know how to use it VERY well, have provided a role and seasoned it quite well, but still not completely accurate)

My goals are either to:

• Break through this stupid barrier which is holding us back from a healthy relationship moving forward
• Emotionally Distance myself from her (cant do no contact because of kids, i'm already doing smart contact) because she seems to be reluctant to want to open up... Shes waiting for time to magically change her mind to open up
• Help managing my emotions and processed with moving on because of her stupid behavior and reluctance to open up... I wont allow myself to be put through this pain forever, and soon the time will come where I'm better off just throwing in the towel.

If i'm missing context, i'll add to it later after some comments