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You can petition the family court to change the children's last names.
As you probably already know, once the papers are filed with the court you are required to serve a copy of the papers on the biological father - even if he is currently incarcerated. He will have the opportunity to reply to your request in writing or by making a court appearance. (The jail/prison would arrange transportation, etc. if it were necessary for him to appear in court. His attorney would help him with these arrangements.)
Ultimately it is up to the judge to decide whether he will permit the children's' names to be changed or not. He is going to consider what is in the best interests of the children. Unfortunately, unless a child is around 12 or 13 years old the judge will often not even listen to the child's wishes as it is believe that a child younger than this cannot know with any certainty whatsoever what is in his/her best interests. Even a child of 12 or 13 can be heard by the judge, but most judges will give the child's words very little weight.
What the judge will consider are your reasons for wanting the names changed, your ex-husband's reasons for opposing them, his past, current, and potential future relationship with the children, along with his behavior/character, etc.
It is very difficult to predict what the judge will do given that the rape occurred almost 20 years ago. Much will depend on everything your ex-husband has done since including his behavior while incarcerated, if he has been released what he has done since, his visitation with the children since the divorce, and evidence of his relationship/abuse of the children while you were married, etc.
Ultimately the judge would have to decide that despite your ex-husband's protests, it would be in the children's best interests to have a new last name. Some of the reasons a judge might choose this is if the father had very little contact with the children, was of "bad" character (i.e., has recently been convicted of other crimes, abuses drugs, etc.), the children's knowledge of their father and his past and current behavior, etc.
Also, after you are married you might want to consider seeing if your new husband wants to adopt the two children. This will often result in the court terminating your ex-husband's parental rights. Doing this would allow you and your new husband to change the children's last names. However, even if the judge permits adoption he will not allow termination of parental rights if he sees that your ex-husband is involved with the children emotionally, visits them as often as allowed by the courts, etc. If he chooses not to visit them and is not involved with them then a judge will often terminate parental rights along with an adoption regardless of the parent's wishes. (Actions speak louder than words - so opposing termination if he has deliberately declined opportunities to see the children, speak to them, etc. would suggest to the judge that the protest is out of spite and not due to any desire by the father to be involved with his children.)
In the end, there is no harm in petitioning the family court, making your best arguments before a judge, and letting the judge decide. If the judge will not allow the name change then at least you tried. If your husband cannot got his act together enough to even show-up in court when he is supposed to, you can potentially win if he defaults.
Please let me know if you have any questions about this.
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