A paternity test should put an end to this, as you should have substantially less than the 50% genetic similarity used for paternity testing, due to only sharing half of your brother's genes (and he only half of his child's genes). One possible outcome is that she sues you for paternity, you get tested, and that's the end of this, as ridiculous as it may be.

However, given that her conduct has included deliberate attempts to get around barriers and involves coming to your home, a restraining order might not be out of the question. Call the cops, as instructed, if she comes to your house again, as well: that's a strong indication the police think she may be dangerous, too.