Girlfriend (25 f) dislikes my (30 m ) relationship with my baby sister (10 f)

I am very close to my baby sister. We share a father, but not a mother. My dad, is kinda a flighty guy. As a result, I?m more of my sister?s dad than he is. I have her so often that I have a two bedroom condo and every house hunting venture lately considers her.
My girlfriend of six months doesn?t like that she?s always at my house, that she has a room, or that I do her laundry. My girlfriend was putting sheets on my bed and there was a pair of my sister?s underwear that fell out of them obviously tangled in the dryer. She lost it. She was saying our relationship is weird and I have to stop having my sister so much. Honestly, that?s not gonna happen. I love that girl, and I?m basically her dad. So I need advice in telling my probably soon to be ex that.
Tl;dr girlfriend is jealous of the time I spend with my little sister and basically insinuates it?s inappropriate. How do I tell her to chill? More importantly, how do I keep her from telling other people that?
Edit: we did sort of fight when she said that. I told her my sister is the age I was when my mom died and I had to go live with my dad full time. I wouldn?t wish that on any child. She knows my mom died horribly and I think she knows the impact it?s had on me


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