I'm not really sure what #1 is going for with " let her know that she hasn’t violated a family rule by not eating all of the food on her plate." She has violated a family rule - just not your family's - and that's an important distinction to have!
It's unclear from the letter whether the kid even knows what's going on, though. If you ask the kid how it went and they don't say anything, it might be better to just leave it be - the mom may not have even said anything in the moment, just silently judged your parenting.
But especially if the kid does have anything to say about the other mom's food rules, it might be a good chance to talk to the kid about being a guest and host, and how as a guest you should always make an effort to be extra polite and to be gracious about the food even if it's not your favorite, and so on, and that some houses may have different rules or customs and when you're a guest it's polite to do your best to abide by the other house's rules. But also that as a host you are also supposed to be polite and understanding of the fact that a guest might be used to different ways of doing things, and to be more lenient with them than you would if they weren't a guest. And that not everybody is good at being a polite guest or a polite host but as long as you've done your best to be polite, the other person's rudeness isn't your responsibility. And so on.
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It's unclear from the letter whether the kid even knows what's going on, though. If you ask the kid how it went and they don't say anything, it might be better to just leave it be - the mom may not have even said anything in the moment, just silently judged your parenting.
But especially if the kid does have anything to say about the other mom's food rules, it might be a good chance to talk to the kid about being a guest and host, and how as a guest you should always make an effort to be extra polite and to be gracious about the food even if it's not your favorite, and so on, and that some houses may have different rules or customs and when you're a guest it's polite to do your best to abide by the other house's rules. But also that as a host you are also supposed to be polite and understanding of the fact that a guest might be used to different ways of doing things, and to be more lenient with them than you would if they weren't a guest. And that not everybody is good at being a polite guest or a polite host but as long as you've done your best to be polite, the other person's rudeness isn't your responsibility. And so on.