Chloé's issues with Audrey affect how she sees girls that she believes are more strong & popular than herself.
There's the obvious case with her fangirl crush on Ladybug in earlier seasons.
Then there's the (not so) surprising case with Alix Kubdel.
Who is quite liked by most of her classmates and other friends...
Even admired abit by Chloé herself.
With these two, she either wants them to see her as this great girl and/or to not see her as some predictable, incompetent, and clumsy dork.
We know about the MANY examples of this when it comes to Ladybug... but it's there with Alix as well.
Like when she clearly regretted dropping her watch...
Lying about dropping it when it was revealed to be a birthday gift/family heirloom...
These moments in Season 2 that happened before and after Audrey's official debut episode...
When she doesn't physically hurt Alix while she was on the ground and laughing at her Queen Banana idea...
She's even close to Alix before and after Ladybug shows up during a couple of akuma attacks.
Chloé's mommy issues makes her want to impress strong and popular girls who want NOTHING to do with her (in canon).