I grew up in a household that manners were of the utmost importance. You could be grounded for talking on the phone if you didn't answer it properly. In some ways, in that respect, I have become my parents! My father and mother were truly the most mannerly people in my life and great role models. Children can implement manners at a very young age and understand the concept of them too! My children are almost 14 and 11 and they have very good manners. You are right about enforcing them - you may have to soften your approach, though.
Usually in the summertime, I will have 4 or 5 kids, daily, at a lunch table. I pass out lunch to the first one, who may say "thank you" and I comment "how mannerly the group is -which the rest always follow suit. Or... the first child doesn't say "thank you" but I ALWAYS say "your welcome". When the kids were younger, a friend would say, "But, Mrs. P.... I didn't say "thank you???" to which I reply nicely - "Oh, but I ALWAYS have to remember my manners." I missed greeting one of my son's friends, one morning, at the bus stop and my son called me on it, later in the day. I call all the kids in the neighborhood by name. Kids do know.
My children know that when we serve people at lunch or dinner, the guest always gets served first and the "server" gets served last. When we leave a store, the first person "IN" opens the doors for the rest. I am always quick to comment on how mannerly that person is. A gentle reminder to the first person - "Are you holding the door for everyone?" usually cues someone to do it.
Do your best NOT to point out the bad behavior - praise the good behavior. Kids want the attention and usually "good attention" is better than "bad attention".
Every now and then, when the kids were younger, we'd play a game at the dinner table (Dad usually wasn't home for this!) I called it "the penny game". Every participant received 5 pennies. The goal was to win EVERYONE's pennies. Usually the kids would play when we had their friends over (and the friends would request it.) If you "Catch" someone being unmannerly (i.e. eating with their mouth open, interrupting, not saying please and thank you, reaching in front of someone, singing at the table, getting up without saying Excuse me - and upon returning, not offering to get anything for anyone...etc...) someone would call the person on their ill behavior and get one of their pennies. (And I would do something blatant - like burp or play with my food!) It really did help them.
You are doing a great job enforcing her manners. It is so important. It's sad that there are so many adults who lack them. Criticizing her parents will get you nowhere! Telling her parents how mannerly she is at your home (while she is in front of you!) will speak volumes to her, when she is being mannerly. Patience, patience, patience! I promise that it will pay off. Good luck!
EDIT: You mentioned - talking with food in their mouth... my response is: "Oh... I really want to hear what you have to say so let me know when you are done chewing so I can listen" ...sometimes if they are at the end of chewing - I will say "oh... I'll wait until you are done... " and then I HAVE to wait. (then... you watch them chew their food quickly because they know they will get your full and undivided attention!) You have to do this strategically otherwise your meal will ALWAYS be cold when you eat!