Not to sound mean about her, but this isnt about her rough childhood. Its about YOUR wedding. You deserve to be a little selfish! You will never have either wedding. If something does happen at the wedding, you will never get that day back. I would tell her to shape up or not bother. Everyoen else is paying a lot of money to come as well. They deserve a stress free vacation as well.
If she is having problems with booze at the moment and does do something drunk and stupied during a toast or something. When she is older and sober, she is going to hate herself for it. Trust me, I use to have a real drinking problem and have big regrets with people I have hurt.
If you do keep her in the wedding and have her give a speach, get her a gift...but don't break the bank on it. If she is drinking at the wedding, you don't want to give her another excuse to be mad at you and cause a scene.
Because she already paid, maybe offer to pay for the cancelation charge.