How can you say one of the marks of the Church is unity when at one time there were three popes?

Your facts are wrong. There never were three popes at once—and never two at once either. But there were times when there were two claimants to the office, and once, in the 14th century, there were three claimants.

The question then is: Who was the real pope? No one at the time thought there could be more than one.

Consider an analogy from recent American politics. In a close election, one might ask: Who is the real president? Even if the answer remained unclear for a while, we’d all know there can be only one president at a time, even if more than one proclaimed himself the victor.

Incidentally, these days the college of cardinals stays locked up together until any ballot disputes are resolved. Not a bad idea, that.