Matt, First off, Welcome!
Sorry, but my vote would be to send her on her way packing. If after all you've done to try and teach her how to behave around Ponti, she still won't listen to you, then she is disrespecting you and Ponti. If she continues with her behavior around Ponti, then Ponti will turn into the bird you describe.
I know you want to help your cousin, and that's wonderful, but she will continue with her life in whatever manner she chooses, Ponti doesn't have that choice. Sorry, I'm not being helpful on this issue. It's just my opinon and what I would have to do if I was in your situation.
And I would be fearful as you are, of leaving them alone for any lenghth of time.