I think you need to really lay out your case in your own mind right now. Be prepared to explain your actions.
Also validate her concerns, she'll have plenty I presume.
But if your actions are truly in the best interest of your children, and you can explain it clearly, I believe she will eventually understand. Don't expect it right away though.
Let the L's handle as much as possible. I won't sugar coat it, this is going to be tough. Stand tall and be proud you are being the best dad you can be.
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Happiness is not something ready made. It comes from your own actions.