You were bang correct with the 1st iteration, I think I will also call her Analis from now on!
The reason I called it a dumbass song is explained in the video, but the short version is that the stupid bitch clearly does not know what "ironic" means. Not one of the things she references in it is an example of irony.
Rain on your wedding day - not ironic, unless you're marrying a weather forecaster who predicted that the day of your wedding would be sunny.
A traffic jam, when you're already late - not ironic, unless you're a town planner & you're late for a seminar of town planners & you were giving a talk on how you solved traffic congestion.
As Ed Byrne states, the only thing ironic about that song is the fact that it's not ironic & is written by someone who clearly doesn't understand what ironic means.