Enrolling my wife in a firearms/self defense class really opened her eyes, and changed her perspective.
We took the class together, and as I recall, her "light bulb" moment was seeing a video demonstration of how easily door locks could be defeated. She realized she wasn't as safe as she thought, even at home.
She was raring to go hot after that.
Granted she wasn't as strongly opposed as yours, and didn't lay down any ultimatums (she'd been to the range with me a few times, but didn't understand why she "needed to learn"). She now has a CCW and carries occasionally (still working on this)
BTW, if you've purchased the gun in spite of her threat, then it appears you've already made your choice....
I'd personally call her bluff, then go from there. I suspect there will be some raging....maybe even a few nights on the couch, but hopefully it will blow over.
NOT A MARRIAGE COUNSELOR