You didn't fuck up. Your step-dad did by being an all-around narcissistic, manipulative piece of shit. I empathize with your mother because it can be very difficult to leave an abusive relationship, but at the end of the day you also have to think about your own safety and future. You shouldn't force yourself to live in an abusive environment because it's more convenient for everyone else.

Hopefully this will be the wake-up call your mother needs. Some people don't change and if he's like this now, think about how he might be 5-10 years down the line. Only a real toxic piece of shit would stop a mother from having a relationship from her own child. I know that moving on is never easy, but sometime being a parent means you have to make difficult sacrifices for the future of your children.

Also you never know. In a few years time she might meet the perfect soulmate. Life is too short to spend it with someone who doesn't respect you or your family.