MB here - our nanny clogged our toilet a few times and never told me. I just discovered when I went in there! Honestly it wasn't that big of a deal. I just plunged it and didn't mention it. Not sure anyway if it was her or our toddler. I did at some point just casually ask her to make sure DS wasn't flushing too much TP or wipes or anything, but otherwise we never discussed the true source of the clogs

I don't know about other people, but I would much rather someone leave the clogged toilet than try some hangers/soap/etc. I think it's fine to try that stuff on your own toilets but I've known people who did more damage with home fixes and I would be more upset if something happened that required a more extensive repair. Plus if you're elbow deep in the potty, you're not watching the kids. Seriously, any mom has probably seen and cleaned up a whole lot worse than a clogged toilet so I'm sure it's a bigger deal for you than for the family. I totally get being embarrassed though. I'm sure anyone would feel the same way!