"want to know a quality of a girl? Get to know the mom" -my dad
Sometimes you're better off not knowing some family members. As genuine as you may seem you just can't impose yourself on other people and their families. Especially people you don't know. They may not be ready. Ever stop to think that... I dunno they really don't think highly of your half of the family?
The reason I say this is because I'm so familiar with sibling fallout stories due to the separate moms. You are the victim of a huge web of drama that you haven't even scratched the surface of... and her reaction was proof.
My honest advice is just lay off and not provoke the issue. If it's meant to be in the future it's meant to be.
I'm sorry for being so blunt. I really am.
I am the black sheep 
"of course I'm crazy, but that doesn't mean I'm wrong."-Robert Anton Wilson
