Rant about my half-sister

I hate how my mom acts like my half sister (dad's side) isn't part of the family. It's like she expects my dad to value me and my "whole" sister more than her. My half sister doesn't love my mom, but she still respects her as a step mom and everything. Meanwhile, my mom calls my sister her "husband's daughter" and is just weird about it. She has known my sister for her whole life and I just feel like it doesn't make sense. I don't know if she's worried about my sister's mom and my dad, but it's just weird.

Sorry if this makes no sense lol