This sounds like a good solution. What a nightmare and a real power tug-of-war.
Kind of reminds me when I was visiting my grandmother and my dad's sister, whose hair was a different texture from mine, decided that my hair didn't have enough "sheen." And then she proceeded to unload half-a-jar of Ultra Sheen on my head. I looked a hot mess. A greasy hot mess.
But the difference between my situation and your daughter's is that I could wash the grease out. As others have noted, your SIL could do serious damage to your daughter's hair.