Should I invite my stepsiblings to my wedding?

My dad has been married to his current wife for 10 years. He has my sister and I and she has three children from her first marriage. She has never been nice to me, neither have her children. To really condense long and sordid stories, here's just a sampling. Her oldest is an alcoholic. She always yells at my dad constantly demeaning him while her mother stands by and supports her because "she's had a hard life." My stepmother’s other children have similar issues. One is a drug dealer who deals out of my childhood home. The third has mellowed as an adult but once pulled a knife on me when I was trying to go into another room. As a teenager I was frequently kicked out of the house because her children were unhappy with my presence. I’ve tried to just let it all go, but it’s hard to forget. A few years ago her daughter graduated from college. The entire family, extended and otherwise went out to dinner, including my dad. My sister and I were not invited, even though we lived in the same house. When we asked my step-mother said it would have made her daughter uncomfortable. We were very hurt by this, I always hold out hope that something will change but now that I'm truly grown and have a life separate from them I feel I need to draw a line. To protect myself from the hurt they have caused me for once and for all. I have decided not to invite them to my wedding. I do not want to have that day based on their exploits and drama and it's unavoidable where they are concerned. My stepmother is invited, this is solely about her children. My dad says I should invite them because they wouldn't come anyway, and if they did they would only come for the free bar. My fiance and I and his family are paying all the wedding expenses. My mom died two years ago and that makes it even more important to me that my wedding day involves people that love me, care about me, and respect me. Am I wrong to not include them? Should I change my mind?