try clearing your cache/cookies, using another browser, and completely restarting your computer. This would also explain why the other users aren't seeing this in their notification bar, as it sounds as though they're not successfully being sent.
If that still doesn't help, you might also want to try reinstalling the plugin according to the steps here.
To answer your other question, you can also take the URL from the Hangout itself and send it to the desired people/Circle via a Google+ post, chat, email, etc. They simply need to copy/paste, click that URL and they should see your Hangout.