Don't want my husband around his sister

I'm really trying not to be controlling but I don't have a very good feeling about my husband's sister. Backstory on my husband is he didn't have a good childhood. He has a twin sister and he was actually a surprise. His parents just thought they were having one baby and didn't go to doctors appointments like they were supposed to. His parents treated him very different from his sister. He was abused a lot and his sister participated in this abuse and bullying towards him. She and his whole family was awful towards him. So he moved away for college. Got a free ride because of his grades, he makes 6 figures now. We got married last March. Have big house. We are expecting our first baby. Basically he's doing amazing and made it past all the abuse. His sister on the other hand has gotten worse. He has tried to forgive her for how she treated him when they were kids but if I'm gonna be honest, she's extremely jealous of him. She has nothing. She lost custody of her kids to her ex. Has been homeless. Has been on drugs. She has said awful things to my husband AS AN ADULT! That he doesn't deserve his life. That he's trash and will always be trash. Spread rumors that he hooks up with men off the street and has HIV. Really weird stuff. The last time they saw each other we had to have the police arrest her for assault because she scratched his face and told him she wished he died in the womb and kept hitting him in the face. She has told him she wished he died several times. That was the first time she attacked him. He has her blocked but he received an email from her with the exact same bullshit she does Everytime. The I'm sorry. I was in a dark place. I'm back in church and I'm doing better mentally and want us to be close again. She's given that exact same copy and paste apology like 8x times. So they talked through email and it made me uncomfortable how much she was asking about our finances and how much money he makes. She wants my husband to come down and visit her but maybe I watch too much true crime because honestly that sounds like she's gonna murder him. And I don't want her at my house! I'm not sure how to not sound like a controlling wife but I just think he needs to cut his loses

Edit: Whether or she's sober honestly doesn't change her much. She's awful when she's sober. She's awful when she's on drugs. Honestly prefer her when she's on drugs because she leaves us alone. Half the awful shit she's done she's been sober for

Edit 2: Never said sobriety as a whole doesn't matter. I said FOR HER whether or not she's sober she's awful. She's awful to him when she's sober. She's awful to him when she's on drugs. At least when she's on drugs she isn't out trying to ruin his life or tear him down more. Some people are bad people regardless of drugs and she's one of those people.

Edit 3: We are discussing therapy. He's a little nervous because he has a hard time opening up about his feelings but he's becoming more open to it