What are the different feelings that occurred when the children were kidnapped?
This is actually a really good question (and kind of a trick question) because the different characters in Where are the Children? feel differently (and react differently) because of the original kidnapping of Peter and Lisa. I will assume it is the first kidnapping you are referring to because that is what most of the novel centers upon.
The "different feelings" exhibited by the various characters are revealed at different times during the novel and run the full gamut of emotion from desperation to elation. First, let's take the main character, Nancy, the mother of the two children kidnapped. Nancy's reaction is one of both desperation and grave concern. Even though, throughout the course of the book, Nancy is revealed to be mentally ill herself, she is not the murderer. Her reaction is a "normal" reaction of a grieving mother, especially after she finds out her first two children are dead.
Carl, Nancy's first husband, is what I would describe as "elated" about the kidnapping and killing of the children. Why? He is the kidnapper. Because the deranged Carl has been molesting Lisa, Carl is forced to kill both children to cover the crime. This is definitely an example of situational irony, though, because the reader is lead to believe that Carl has committed suicide as a result: suicide out of desperation. Really, Carl is faking his own death in order to cover up his deranged behavior.
Another character of note is Rob Legler who is the one chief witness. Rob, of course, was a student of Carl's at the college and falsely testifies against Nancy at the trial. The main feeling that Rob feels when the children are kidnapped is fear. In fact, he is so afraid that he flees. (As a result of this, Nancy cannot be acquitted.) A further reason for Rob's fear is his AWOL escape from the army.
In conclusion, the reason why your question can be considered a trick question is because Nancy's second two children get kidnapped as well, and Nancy's reaction (due to her previous ordeal as well as her mental illness) is even more frantically desperate.