A driven mum must rise above her own insecurities to prove her inter-racially adopted daughter loves her.

The threat of losing her daughter sounds like what sets this story in motion.

Story: Cause; the threat of losing her daughter > Effect; The lead must rise above her own insecurities > Conclusion; unknown, maybe she succeeds maybe she fails.

Therefore what or who is threatening to take away the lead character's daughter should be added at the beginning of the logline.

To help with the hero’s desire, jot down what the viewer will be watching for the majority of your film, then find that relevant inciting incident to get your logline’s bearings.
For instance, I had no clue this involved a troubled teen, I was on the - mother raising an adopted interracial youngling timeline.
Based on your feedback, one angle for this mother is to overcome a toxic upbringing to be a role-model for this teen. You could use Mike’s mentioned road trip if you have not already established your story beats.
Keep going, take care.

So not to lose her daughter.