“And of course, John Kerry had his first marriage annulled, not merely a divorce. So now in the eyes of the Church both his daughters are illegitimate…”

No they’re not – not in the Church’s eyes or anyone else’s. The term used regarding annulled marriages is that it was a “putative” marriage – that is, believed at the time to have been made in good faith, and binding.

The rules regarding annullment are too lengthy to go into here, and since we don’t know the details of Kerry’s, I have no idea whether it was a genuinely invalid marriage or whether (like Henry VIII and certain people named Kennedy) he wanted to get rid of his wife and have a clear conscience while doing so. Either way it has no effect on the status of the children.