A religious annulment is a process in the Catholic church. It only affects whether the Church recognizes your marriage - not whether it is legally binding.
Now if you are talking about a secular annulment (which I can't imagine would be the case since the original marriage was obviously consummated because they have children), then yes Kerry would be a bigamist. Is that what you are suggesting?
Rationalize it all you want but it is NOT Biblical and is nothing more than a DIVORCE for money without the label.