Thank you for your thoughtful reply. Your argumentation is correct, no doubt about it.
If its about making kids she is all over sex. Avoiding sex is about avoiding emotionally bonding to be to avoid being hurt.
She is most of the time an exceptionally loving mother and the kids love her as much as I do. Our kids need both parents in their life and making that decision would hurt my kids and the woman I love. I have always said, that the day our kids lives are more impacted by my staying than leaving (because of ongoing conflict) I would leave.
Pressuring her won't solve this conflict sadly. People only chance through their own volition which makes this tricky as she has no real incentive to change.
Im also the sole breadwinner and although I earn good money, the local cost of living is too high to keep my kids lives strable if I need to finance separate accommodations. They would need to move and change schools and friends and I'm not willing to go there just for my well being.
Trying to "take the kids" is also a gamble. Even a progressive country like Germany seldomly awards full custody to a man. And again I'm not willing to hurt her or the kids by separating them from their mother.
Its mostly a stable and safe life for my kids. Her refusal might change, or might not. But considering all the things as they are, separation would hurt all the people I love including myself.
I have recently tried looking for therapy for myself to help with coping with all this and I'm waiting for what life throws at me next.