I feel like this is what's happening in our household. We have a son at home, he watches a ton of youtube, and here and there he'll emulate what he sees others doing on there. Some of that is AAVE, words, pronunciation, etc, often from memes. And we tell him off for that, because it's not his culture or background. But at the same time, I feel like that creates a stronger divide, an "othering" of sorts - as in "we are not like them", instead of our intent of "you should not appropriate or make fun of African-American culture".
Honestly, everyone should read this article about cultural appropriation[0]. I don't really know if emulating AAVE is "cultural appropriation" unless it's used to cheapen or degrade people, particularly black people you come in contact with, as you say is your intent.
I feel like that's a lot easier, the copying this or that saying isn't really an issue, it's more of respecting people right? That's easily a universal good that isn't hard to understand and gets directly to the underlying issue rather than surface level prescriptions for behavior (don't copy this language, etc).
Using AAVE is not the same as mocking AAVE. That's just how language works, you adopt what you hear. Telling him not to speak like his friends and the people whose media he consumes is an exercise in futility.
There's some good stuff floating around on the 'net about, for lack of other terms, cultural adoption and celebration, versus cultural appropriation. IMHO the nugget that distinguishes one from the other is whether the thing is being severed from it's origins, or whether what you're doing with the thing is connecting yourself to it's origins.
