That's where the passive agressive part comes into play, she's always fighting with Kirito even Asuna notice they are always "bickering" with each other.
Well Inoda will outplay her that's given, if not in this update the next one for sure, i sttil think her plan will backfire on her and she will endup fucked by Inoda, most likely because he will use her ideas and information about Asuna but will not follow her plan which he called "nonsense bs" and because of that her plan will fail. So far they have a common goal, Inoda knows she is using him to break them apart, but for that to work for her Kirito will need to know the truth and in this point Inoda will not follow the plan because it's a risk for him, if this happens Asuna will tell him to fuck off because Kirito can't know about the affair.