She's right to get angry. There's nothing special about 432Hz (see my comment above on it's absolutely arbitrary nature), BUT the numerology that falls out of musical harmony is is indeed special and makes most of human race happy because of the aesthetic satisfaction that Pythagorean harmony (or even it's equal-tempered cousin) delivers to people.
Science is very good at describing things and why they're interesting, but science can't tell you what's beautiful or how to live. I understand your desire to point out the meaningless nature of setting up 432hz as some gold standard and agree with you that it's nonsense, but a spoonful of sugar helps the medicine go down' you could invest more time in exclaiming over the beauty and meaning of the relative pitch relationships in music, the most popular of which happen to nicely (albeit slightly inaccurately) mirror the ratios of planetary orbital periods. Your sister has the right idea in the wrong context, and you're missing out on some aesthetic insights by overlooking this.