I'm a stepfather, but didn't have a situation like you're dealing with. I stepped in as the father figure for my daughter when she was 9. Her real father bailed out the minute my wife got pregnant.
As one step-parent to another, the problem you're having with the children is only the start though. You'll be fighting an uphill battle their entire lives. Get used to being listed as only a "Non-Family Emergency Contact" on their school paperwork. Trips to the hospital can be a nightmare too, admittance and visitation can be a pain because you're "not family". Seriously, an unfit, abusive mother or dead-beat dad ranks higher in the eyes of society than the step-parent who's trying to make things right.
I wish I had good advice, but becoming a step-parent is, in my opinion, the toughest job anyone will ever take. It takes a special kind of person to take in a child that isn't biologically theirs and then fight against society and the world to try to raise the child as their own.
But it's a war worth fighting.