Sounds like she was a piece of work! I would simply diffuse any comments made like:
"I am always in compliance with ratios" or
"This is a food program-approved meal" or
"If you prefer, you can send in food for her daily. There is no tuition reduction for this option and it must meet Food Program and MyPlate food guidelines with 0 junk food or treats" or
"Ok, say bye to mommy!"
A lot of times us providers with big hearts don't say anything or show parents where their place is, out of fear, but this is how I would've responded to her comments. And had that be the end of it. I don't tolerate sass and it's in my policies that if they are disrespectful or menacing that it's grounds for immediate termination.
But you definitely did the right thing. How can they tell you not to give the paci but then they give it to their child right at drop-off and etc? laughable!