OP you need to understand that your decision to not invite your new daughter to your wedding WILL have consequences. It will cause (perhaps irreparable) damage to her relationship with you and her own father. It will also damage her sense of self worth, most likely for life.
Are you willing to jeopardize life-long consequences for your new daughter against having a fun, stress free party that lasts exactly one day?
I get that she is being difficult. I teach high school, but I used to teach seventh grade so I get how terrible 12 year olds can act. Especially, hurt 12 year olds. You just have to remember that you are the adult and soon to be parent in this relationship. You cannot look at this situation as "you against her". This attitude will be disastrous for both of you and will never work at improving your relationship with her.
May I suggest a book for you? How to Talk to Teens so Teens Will Listen and Listen so Teens Will Talk is one of the books I read early on in my teaching career that helped me build relationships with troubled teens.
You are a good good sister. Do you have a formal diagnosis for her? I have a few good books: This is my top favorite: How to Talk So Teens Will Listen and Listen So Teens Will Talk https://www.amazon.com/dp/0060741260/ref=cm_sw_r_cp_api_i_FzRzFbF8X18PN Fly lady.net has a great organization website for free, that can help you negotiate routines & life skills that she may not have gotten with all the stress at home growing up.
Can't recommend from experience but I've read How To Talk So Teens Will Listen & Listen So Teens Will Talk and found it had great communication advice so hopefully it's helpful in practice :)
How to Talk So Teens Will Listen. Its about listening, empathy, communication, relationship-building, and problem-solving. Especially important if you think your parents' "strict parenting style" might be causing stress and a rift in the relationship between your parents and siblings (been there, done that; my parents were also immigrants and very old-school). Kids who don't feel respected or heard are rarely inclined to respect or hear others.
People mentioned How to Talk So Kids Will Listen... but there's also How to Talk So Teens Will Listen... :)