By being cool, patient, and compassionate. Own your mistakes tell her from the heart and be prepared to walk away after you do. The point here is to plant the seed not plant it water it and watch it grow all at once. Plant it and walk away.
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How do I let her know that things will be different this time?
Through actions not words. Be the change you want to display.
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How do I put her fears to rest that there will be no reprisals for returning?
Patience and consistency through your actions and through the way you validate and really understand how she feels. If you don't trully understand the problem everthing else is just show.