My suggestion is example. Do not preach. Do not campaign. Demonstrate what a gun owner should look like. Answer questions with complete, unbiased, fact based accuracy. Promote accurate facts above all. Do not argue. Do not debate.
Be the gun owner that is the example we all want. They are afraid, allow them to be afraid. If you believed what they believe and your knowledge was as limited as theirs is, you would be afraid, too. They will see that you are not afraid, and they will want to know why. The answer is not "I'm not afraid because I have guns", the answer is you're not afraid because you have facts.
Different opinions and the people who hold them are not enemies. Ignorance and fear are the enemies.
It works.
She occasionally claims to own a gun, and more importantly her decisions and her votes are no longer based in fear and ignorance.
And finally, if someone looks at the same set of facts as you do and draws a different conclusion, so be it. That is their right, and their rights must be respected the same way we demand that our rights are respected.