Hi, I'd like to help you with your question.
Your hurt over the relationship your children have with their father is understandable. He was abusive and it sounds like he never took ownership of what he did and tried to make amends. He left you with the children and did not do his part to help raise them. Not wanting to be around him or see him is completely within your rights. You are under no obligation to do so, either.
However, your children see it differently. I have no doubt they care deeply about you and probably understand pretty well what you feel about your ex husband. But you have moved on with your life and they need to too. In their point of view, this is their father. Even when abused children still, in most cases, gravitate towards their parents as adults. Very few children have the ability to cut their parents off completely. And your ex may have apologized to them at sometime (they could tell you if this is so or not). They developed a relationship with him that they did not have as children. The benefits of that relationship may outweigh what happened in the past. This does not mean in any way that they care less about you. They just also care for their father.
The issue here is not so much what they are doing but how you still feel about what your ex did to you. If you have not had a chance to work out your feelings, you may still feel the same as you did when you were in your marriage with your ex. You can carry those feelings for years without resolution.
Have you considered talking with a therapist to work on your feelings? A therapist can help you pinpoint exactly how you feel about what happened to you and help you find ways to heal. It doesn't mean it won't still hurt, but it will be much more manageable and you can finally feel free from the marriage you had with your ex.
To find a therapist to help you, try talking with your doctor about a referral. Or, if you attend church, your pastor can help. Also, you can search on line at http://therapists.psychologytoday.com/rms/.
You can also help yourself. Try some of these resources to get started:
Healing the Scars of Emotional Abuse by Ann McMurray and Gregory L. Ph.D. Ph.D. Jantz
Healing the Trauma of Domestic Violence: A Workbook for Women (New Harbinger Self-Help Workbook) by Edward S., Ph.D. Kubany, Mari A. McCaig and Janet R. Laconsay
Do your best to not express your feelings to your children. You want to avoid having them feel they have to hide their relationship with their father. It is ok, however, to let them know you appreciate the relationship they have with him but they are not obligated to tell you what they do with him. That way, you have time to work on your feelings without the fear of being re injured each time you hear about your ex.
I hope this has helped you,