Court ordered visitation is a strain on the whole family. Routines are disrupted, and kids have to keep adjusting and readjusting to two homes. In many cases, the non-custodial parent gives up contact with her kids altogether, rather than subject herself and them to the tension between her and her ex.
People do things to each other during divorce that cause lasting bitterness. If the marriage ended because of an affair, the hurt is enormous. Most of us would sympathize with the wronged party. No one can blame him for being hurt and bitter. It is heartening to know that your kids are on your side, and it is tempting to do what you can to keep them there.
Your kids may support your anger towards their other parent. After all, her indiscretion did cause their family to shatter, and brought the world crashing down around them. It is understandable that they don't want anything to do with a parent who put her own pleasures ahead of their security. If it hadn't been for her, the family would still be together, and the kids could have avoided the pain and sadness they are now feeling.
The kids' welfare is more important than the hurt feelings and anger they may feel towards their other parent. Despite your justified anger and disappointment in your ex, the kids still need to know and love him or her. Yes, she did wrong. There is nothing more damaging to a marriage than a partner who sneaks around, or engages in other activities that are selfish and against the interest of keeping the family and the marriage strong. After all, there were vows between you and your ex, and she promised to put your life together before all other temptations. Nevertheless, your kids have nothing to do with the quality of your relationship to your ex, and it is they who are being punished for her betrayal of the family.
Even if your kids tell you they want nothing to do with their absent parent, their sentiments are likely more of a reflection of their desire to support you in your pain than any real wish on their part to be permanently estranged from their mother or father. They love you, see you are hurting, and feel the only way they can show their loyalty to you is to reject the person who caused your pain.
What they are rejecting in reality is half of their own inheritance, and an opportunity to be loved and protected by the only other person who has a legal and moral obligation to care for them. That security is a lot to take away from the very people who are already suffering the most from your divorce. The kindest thing you can do for them despite your own pain is to encourage them to forgive their other parent and keep her in their lives, even if doing so seems impossibly painful.