I think there are two sides to the coin.
On the one hand, there's nothing wrong with wanting your mother to have less inflammation/etc in her final years. but on the other hand, you have to have her involvement AND that of her support network (which is not you, because you are so far away).
If your sister, on the other hand, had suddenly decided that wheat was out (for example), and she was in charge of mom's meals, and mom wanted all kinds of sweets all day long (ie, cookies), then GF cookies could be made and perhaps she would see some health improvement.
but at the end of the day, if you try to drive this train from 500 miles away, it's going to end in a lot of frustration and anger for you and your family. People will take thing personally, get angry, and so on.
I also can understand that you feel frustrated -- frustrated that you want to help and can't, frustrated that people likely won't listen to you, and frustrated that your mom is deteriorating.
I get that. For years I struggled to change my family's eating patterns and habits. I started to recognize the emotional eating patterns, the negative relationships with foods, and of course, the unhealthy foods that they eat. And, you might even say, food addictions.
Anyway, end of the day, no amount of me talking or mentioning it was going to change a thing. Nothing has. Seriously. It's shocking. And yes, i know that a lot of the things that I do, that I would mention in the past, would have made their daily lives better as well as their long-term health.
But you know what this talk was doing? frustrating them, frustrating me, and everyone would end up angry and not enjoying each other. Food, like politics, is not discussed.