I see a window of opportunity.
Talk to her but don't mention the gun. Talk about how much she and your kids mean to you. How you want them to always be safe no matter what. Tell her there are real dangers out there. How its your job and primary responsibility to keep them all safe above everything (even your marriage).
You take that responsibility very seriously. A gun is simply one tool to assist in assuring you can meet that responsibility.
Along with it, comes education, training and different approaches to situations.
Tell her you want to face these head on WITH HER.
Sign up for classes, encourage her to ask questions, describe the measure of safety you are taking to ensure responsible ownership.
TAKE HER TO A RANGE. I had a wife like yours. I was amazed, it took only one talk, one class, one range trip... She just askede last night when we could get a baby sitter so we could go shooting.
Malo periculosam libertatem quam quietum servitium