If it's her house, it's her rules so maybe get a small safe, show her it's safely stored.
Take her to the range with you, acquaint her with the basic safety rules, let her shoot it for herself. So many people who exhibit "hopolophobia" seem to be cured of this disease once they send a few down range. I can think of one poster here in particular whose mind was changed after her first shooting experience.
Target shooting is a wonderful family bonding experience. It builds trust, respect and maybe even a ittle healthy competition!