wedding invite...sorry the long post!

I need some advice on whether or not to invite my younger sister to my wedding. I am in the process of working on the guest list and I can't decide whether I want to invite her. 
My youngest sister and I were always super close, she confided in me everything, and I raised her for the most part of her life. Until last year, after she separated with her ex, she developed a whole new attitude, she was clearly using drugs, substantial weight loss, change in her appearance, her teeth got to the point they were literally falling out of her head. But you couldn't say anything to her. Being the baby, you could never upset her, you couldn't point out flaws or concerns because she was so spoiled her whole life she would lash out and cut you out. 
My brother and I were discussing one day how we were both concerned for her, and her son, and what we could do to help. He ended up discussing with their mother a way to intervene (my brother and sister have a different mom than I do), and their mom always having hated me because of my mom saw this as an opportunity to start drama. 
She proceeded to tell my sister false statements I made, saying I told my brother I witnessed her verbally and physically abusing her son, amoung other false statements. 
The last time I spoke to my sister, was close to a year ago. The message I received following the lies her mother (who admitted she lied) told her, was the most awful and hurtful things I've had anyone say to me. I was told I was a piece of shit, she hoped I would rot in hell and called me a number of names even going so far as to calling me a coke head. I've never touched the stuff in my life.  After all I have done for her, and her child I was heartbroken. 
I got engaged a few months after this and I never called or messaged to tell her. I told everyone else in my family but her. I don't have her on Facebook, she deleted me, but it wasn't until I saw she liked my picture of my ring on Instagram that I found out she followed me on there. That's how she knew I was engaged. She sent me a message congratulating me, but I didn't respond. 
I decided to try to extend a branch and sent her a Christmas gift and card this year, thinking that might open things up for us, but unfortunately she didn't so much as send a message to thank me for the gift or wish me a merry Christmas. 
After that, I was very upset. Especially to find out she has now moved in with her mother. I did nothing wrong and she won't speak to me or apologize but her mother who admittedly lied, she has a relationship with. 
My fiancé and I are now working on the guest list for the wedding which is happening in July. I'm torn on whether to invite her. My fiancé doesn't want her there as she is unstable, unpredictable and a drug user. But he's leaving it up to me as it is my sister. 
In one way I don't want her there. I feel like the relationship is irepreable, she has made no effort to mend fences with me but has thrown it all out the window when it comes to her mom. And this is my day. I don't want to be worried all day about what she might try to do. Or if she decides to just show up and cause a scene. 
On the other hand, she is my sister and I feel like if I don't invite her it will destroy any chance we may have to fix things. And I know my dad would be upset if I didn't invite her. I've tried to discuss with my mom and she shuts me down. Tells me not to bring it up. That it will upset my father. I was so upset she wouldn't give me some advice and hear me out, that I wasn't going to invite my sister and they didn't have to come either. My brother can give me away. It's my day, and this is important, and I get no support. I can't get advice or have a discussion because it might upset my dad about my sister. Even when she is deserving of not being invited, I get shut down and can't talk about it. It's so angering that she can do no wrong. 
I want the least amount of drama as possible but it seems regardless of what I do I am going to have drama. 
I have to make a decision quick as the invitations are set to go out and I have one not addressed and set aside for her if I decide to have her. I just don't know what to do. And my fiancé telling me it's up to me isn't helping.