The problem with using "coincidence" is that coincidence usually has a positive connotation. Bringing your child to your alma mater after 20-30 years, and coincidentally, your old best friend who you haven't connected with in years is also bringing their kid. While it may not technically be wrong, it feels wrong to assign "coincidence" to something bad happening when you're expecting or hoping for something good/great. That tends to be the place where Irony takes over. Irony may also have the deeper meaning of something so over-the-top unexpected and planned against (firetruck on fire), but if rain on a wedding day is not ironic, then it's not merely "coincidence" either.