Children produced during a civil marriage are not illegitimate. That legitimacy is not affected by divorce or annulment.
Similarly, children produced during a valid marriage are legitimate, and that legitimacy is not affected by later annulment. BTW there are civil annulments.
An annulment DOES NOT say "what marriage". An annulment does not "erase" a marriage.
"An ecclesiastic annulment is a declaration by the Church that a marriage which was thought to be valid was not legally(Church law) binding. This might be because of some defect in the consent given on the day of the wedding, or possibly a defect in the psychological capacity of one of the parties.
When an annulment is granted, the Church is not saying that there never was a marriage. The union certainly was a sociological fact, and the memory of it may even be cherished, but the legal(Church law) contract on which it was based turned out to be invalid.
Canon law declares that all the children born of an annulled marriage are legitimate. The unfortunate designation "illegitimate" is hardly used anymore, but it is technically reserved for those born out of wedlock, which is certainly not the case in an annulled marriage."
Now, as far as Kerry's annulment or not, there is no way he can get an annulment without his ex-wife's knowledge. The ex-spouse of anyone who petitions for annulment has certain rights under church law, even if they aren't Catholic.
If indeed he did not get an annulment, then his current marriage (in the eyes of the Church) is invalid and adulterous.
Thanks. If he was able to get a marriage annulled after having had grown children, then that's a scam involving the illustrating a phoney annulment for political purposes. If he didn't get the annulment then his present marriage affects his standing in the church. Seems either way, it doesn't look good for him.