On My Name is Earl, why didn’t Randy and Catalina get married?

He did want to, and they did actually get married. Although the actual marriage was not placed into an episode. It is assumed to have happened, by which I mean it did happen although we didn’t literally see the marriage happen. It happened during the time that elapsed between the episode you mention, and the next episode after that.

They did get married and a few episodes later, Randy has to try and tell her that he actually wanted to marry her, and that it wasn’t just so that she could live in America. Several times throughout this episode, that I mention, they refer to the two being married. Therefore it is logical to correctly assume that they got married.