As breatheslowlysaid, this is all about translation. In MIL's language, they have words which denote respect for unrelated adults. They have a different word or words for actual aunts and uncles. Somewhere along the line, the "respect" words have been mistranslated as "Aunty" and "Uncle". No doubt goes back to lazy colonists.
OP, have you tried to explain to MIL that, to your ears, calling random adults Aunty and Uncle is the same as calling them [insert her culture's special family word]?
Maybe she'd get it then. Out of interest, was the waiter whom your DD addressed by his first name from the same culture as your MIL? If so, then I am afraid that she was probably right to ask your DD to address him in a way which their culture considers appropriate, just as you'd have told her off for clicking her fingers at him. (Though not right to do it in a way that undermined you).
However if he was not from that culture, she was totally wrong and frankly needs to acvept that she is the one who should adapt to the culture of the country in which she has chosen to live.
Could you compromise by agreeing that DD will address adults from MIL's culture using the respectful term in its original native language form? Even if speaking English that might work OK, just like you could easily say "I was talking to my French teacher Monsieur Roux yesterday and he said..."
That way you don't have to hear her use words that are special to you in a way that sounds inappropriate and the adults who'd expect the respect still get it and don't look down on MIL for having a rude DGD....
Then you agree with both DD and MIL that to adults not from that culture it is NOT appropriate to call them Aunty and Uncle and frankly sounds odd to them as well as to you.
Worth a try?