This is one of Ms. Kennedy's central objections to annullments, and it is wrong, wrong, Wrong! Here is what the Catholic Church really teaches:
There are two types of marriage: natural marriage, which God established in the beginning for the entire human race (Genesis 2:22-24) and sacramental marriage, which Jesus established for the members of His Body, the Church (Matthew 19:3-6). Any adult can enter into a natural marriage, and it can be sealed in any public ceremony: Christian, Jewish, Muslim, Hindu, Pagan - even a civil ceremony. Sacramental marriage is sealed in the Sacrament of Matrimony, which only Christians can receive.
Divorce is the dissolving of a marriage. A natural marriage can be dissolved by divorce, but a sacramental marriage cannot, since Jesus said "What God has joined together, let no man put asunder" (Mt 19:6). Only death can dissolve a sacramental marriage. So if a man in a sacramental marriage gets a divorce he really remains married to his wife in the eyes of God, thus if he "remarries" he commits adultery (Matthew 19:9). That's what Jesus said, the Catholic Church didn't make that up!
Since some people are in difficult marriages, the Church tries very hard to help them, while staying faithful to the teaching of Christ that a sacramental marriage is indissoluble. The Church helps them by issuing an "annulment" (really called a "decree of nullity"), which is a decree stating that a Catholic marriage was never really sacramental in the first place, only natural, and so can be dissolved by divorce.
You see, when two Christians get married, a sacramental marriage takes place unless there was an impediment to receiving the sacrament when the wedding took place, such as no intention to consummate the marriage. or no intention to have children, etc.. If such an impediment existed the Sacrament didn't "take", so the marriage was merely natural, not sacramental.
When a canon lawyer, after a thorough investigation, determines that an impediment existed which kept the Sacrament of Matrimony from being conferred, he can issue a decree of nullity stating that only a natural marriage exists. Then the couple can dissolve their marriage in the courts and later remarry in the Church.
Since an annulled marriage was still a natural marriage, the children conceived in that marriage are perfectly legitimate. The Catholic Church has never recognized such children as illegitimate. Sheila Kennedy should have done her homework before publishing a whole book based on a mistaken view of annullments. It doesn't make her seem too smart.
Why did I give the book two stars? Because I do sympathize with the author insofar as I believe that the canon lawyers in the US are giving out way too many annullments, and are allowing rich, famous men like the Kennedys to abuse the Church's kindness. How many times have the Kennedy politicians publically trashed the Church's teaching on abortion, male-only priesthood, etc., yet when they want a marriage or a funeral they go running back to Mama Church for a church ceremony!
The Kennedy men break God's commandment against adultery left and right, but when one of them decides to trash his long-suffering wife and marry his new honey, he wants a church wedding! That's how this whole annullment flap got started. I wish those in authority in the Church would take a stand against such abuse; if someone had this book might never have been written!