It would appear like the overwhelming opinion is that I should have gone around. This really was my first experience landing when I would have needed to make that decision. Up until this point all of my landings were without incident.
I am going to make it a point to commit to my mind that a go-around is always an option and really work on making it a matter of a split second decision.
From what I can tell, I caused the violent wobbling because I failed to use rudder in coordination with aileron to correct the initial roll.
Thank you for all of the fantastic advice!