I fully expect the players to be snarky to her, so I want to be prepared for that.
Happens to us all at one point or another. It's been my experience some players do it to simply test what kind of game the DM is running (e.g. the Mummy movies where the main character smarts off all the time) and/or because they believe it will make the table laugh and enjoy the game more.
However, it's easy to forget to divorce our personalities from our characters when we're sitting around eating doritos, sipping soda, and going off-topic by discussing the latest movie we watched. Would a character really smart off to the Emperor of All-I-C, knowing it's execution if they do? So, can you have both respect and mouthiness in your game? Absolutely.
Option 1: have a (late) Session 0 and discuss you, as the DM, really want to work on separating character from player to make for a more immersive game. Discuss examples such as roleplaying fear and horror, or awe, and the difficulty of doing that when you're sitting around the table munching on snacks. See if players will take on the mantle of greater immersion into the game by taking more times to think "what would this character, who has emotions, has feelings, can die and can suffer consequences, do in response?"
Option 2: say nothing and work this in-game by changing tone. Give the line "is that you or your character saying that?" when presented with a really snarky statement that would provoke a reaction. And if they say character, impose a natural consequence. The harshest consequence will actually be removing the opportunity / adventure line. The Emperor was offering 10,000 gold for the return of his ward, and snarky player mouths off wanting 20,000 and to make it snappy. The Emperor sighs and dismisses them. Later, they hear through town the head of the ward was sent by the raiders back to the Emperor along with a note "the Ragamuffins live free of tyranny."
It's not the end of everything, of course. DMs know if players miss a dungeon or adventure, it can be morphed into something else. For example, you might create a new adventure in which the PCs feel bad and join with a merchant alliance to infiltrate the secretive terrorist organization, or even join the rebels.
Option 2 can be tough if you have a pre-written or linear campaign. Many DMs fear going off-script because they'll lose the story. If PCs don't take the Strahd line of Ravenloft seriously and laugh at his obsession with Ireena (e.g. "get yourself a real girlfriend, that's lame man"), the game is simply less enjoyable because it's probably not how characters stranded in a shadow world of tortured souls and shades would tend to roll.