As a guess (and this is a newbie guess, so please take this for what it's worth...which is substantially less than $0.02)

Sounds as though possibly a control horn or pushrod on the rudder snapped off, or came out of a fitting....The 'snap' and then dive you describe makes me think rudder, and the popping sound just sorta seems like maybe a control rod 'popped' the inside of the airplane, or a control horn tore loose or something.

I'll be interested to read what the more experienced guys have to say.