Generally speaking, courts will not allow parents who are convicted kidnappers unsupervised contact with the children. Some states have specific laws on this.
If you are asking if the offending parent will have his parental rights terminated, that depends on the state. Most states do not like terminating parental rights unless the parent is a danger to the children. Here, the facts do not show that the parent is a danger to the children--just that the parent took them. Courts want a potential source of child support so that the children are less likely to become burdens on the state. The courts will protect the children from the offending parent, however.
You will want to consult with an experienced family law attorney in your area.
The short answer is that the offending parent has the right to see the children 'supervised.' There are different ways of doing this, and ultimately the offending parent will remain under "supervised" visitation until the behavior is corrected. In other words, the offending parent would have to satisfactorily demonstrate to the court that the threat of re-kidnapping the children no longer exists. Based on these facts, you should probably already have a court order that spells out the specifics. Consult with an attorney if you do not. Best to you in a difficult situation.
The information contained herein is strictly general and should NOT be construed as legal advise, nor to create ANY type of attorney/client relationship. Always seek the advice of a licensed attorney to ascertain the complete facts of your particular case. You can reach me in my Fort Lauderdale office at 954/734-6048. If you liked my response, please "MARK AS GOOD ANSWER." Thanks and best wishes.