I've met several sisters here--in Canada--who immerse themselves in their "white" friends, because that's who they're around most of the time. and, for whatever reason, do not want to be identified as black. Maybe her friends have negative stereotypes of blacks...and that's her way of distancing herself from those stereotypes. Maybe she had some bad experiences in her interactions with blacks, in her past. if that's the case, you can't fix that. AS FOR YOUR NIECE, it's not your responsibility to teach her blackness. stop trying. it's your responsibility to be the best AUNT you can be, to your niece...and to teach her to be the best person she can be. there is nothing wrong with you answering any question she asks you, if you have that answer to give...or if you can find the answer. that doesn't detract from her relationship with her mother...it should enhance it.
You said
stop trying to teach her to be a good little black girl, and teach her how to be a good little girl. the rest will work itself out...
I agree!
even if the mother chooses not to set her up on that path. PLUS, it doesn't pit you against the mother going forward...and possibly having the mother sever your relationship with your niece.