Well, there is not a single correct word to use in an English Bible because the Bible was not written in English. There can be two equally admissable translations for the same phrase. Additionally, the Douay-Rheims was created primarily as an English translation of the Vulgate, so it has a preference for anglicizing the existing Latin words. The problem is that Latin-derived words often have different connotations than they do in the original language.
As a translation of the Vulgate, the Douay-Rheims does well to translate with “to do penance,” as this is a word-for-word translation of “paenitentium agere.” It is a perfect translation of the Vulgate. Additionally, the Vulgate is a good translation of the Greek. If you consult a Latin dictionary, you will see that this does mean “to repent.”
perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0059%3Aentry%3Dpaeniteo
In addition, the Biblical concept of repentance does include “doing penace” as well. For example, there is Matthew 11:20-21 where repentance is linked with acts of mortification.
If it was so great, then why was ‘penance’ changed to repent in the Bible used by the Vatican and other Catholic Bibles? Obviously, something was amiss!
As for ears vs. years, I have found numerous typos in the DR on my phone’s Bible app. Usually, they are obvious so the important thing is just to expect them. Same with the Summa Theologica on New Advent. I imagine that these errors are mostly just mistakes introduced while transcribing from text to an electronic format. For this typo in particular, I could imagine that it slipped by because ear was interpreted as in ears of corn, so it seemed to make some sense in context.