I understand your hesitation but here is what I gleaned from dating like a madwoman after my split.
There is NO NEED for you to fret over the kids. If the lady loves you then she will love your child. If you love the lady then you should be able to love her kids like your own. If her ex is an abusive ass that gets off on making her life hell then you have every right to walk away. If you decide to stay though, think hard. Don't start out with a faint-hearted commitment then run when the ex just doesn't seem to die.
There are many men on the board who have gone to hell and back because they fell in love with a woman whose ex is the lowest form of scum. From what I understand, they toughed it out and really made a difference in the life of their lady and the lives of the kids.
NO ONE WOULD FAULT YOU THOUGH FOR WALKING AWAY FROM A DIFFICULT SITUATION. YOU HAVE THE RIGHT TO BE HAPPY TOO.
If I am not incorrect though, aren't you just getting through a difficult divorce yourself? In that case, take it slow and take it easy. Take your time to get to know and reinvent YOU before you choose anything serious to get into. You owe yourself time to heal.