I have a couple more questions before making a judgment on this woman. How old are the children? How long ago did the relationship with her children's father end? And has she been in any relationships since that have not produced children? People do make mistakes (especially in their early 20's) but they can change. I would be cautious if there hasn't been any evidence of change to this point though.
Everything will be ok in the end. If it's not ok it's not the end.