I learned to check the dictionary for any word whose spelling was unfamiliar to me--and the bonus was that I would discover its other meanings and learn not to use those meanings unintendedly!
Joe, in all my years, I have never heard anyone use "unintendedly"in this context - or in any other, for that matter. I am not saying you are wrong, but I'd be interested in how you differentiate "unintendedly" from "unintentionally".
Yes, few people choose “unintendedly,” but I have always used it for situations that I felt didn’t really warrant the use of “unintentionally” and “accidentally,” which are its close synonyms. These three synonymous words each has a shade of meaning not common to all. “Unintentionally” means a manner done by intention or design, as in “the damage was done
unintentionally”; on the other hand, “unintendedly” means a manner not expected to be such in the future, as in “a career he pursued
unintendedly.” Of course, “accidentally” is inappropriate in both contexts so we can rule it out altogether from this usage.
Just to increase your level of comfort with “unintendedly,” here are some contemporary usages of the word in various contexts:
“There is at least one
unintendedly amusing moment in this 1962 videotape of the Heifetz master classes at the University of Southern California.”—
The New York Times, 1985
“Ash and Lake present their amazing collection of odd (and often
unintendedly perverse) book titles like ‘Suggestive Thoughts for Busy Workers’, ‘The Potatoes of Bolivia’, ‘Who’s Who in Barbed Wire’, ‘Play with your own marbles’, ‘Making it in leather’, and ‘Scouts in Bondage’.—A
mazon.com Book Reviews“On groundstrokes and volleys, grip loosely between strokes, then tighter as you start your swing. If your hand and wrist are getting tired quickly, you're likely to be gripping too tightly between strokes. If your racquet is tilting
unintendedly, you probably need to grip tighter as you swing.”
—About.com, The New York Times Company“Today the mass scenes border at times on the
unintendedly comic, showing as they do hundreds of people moving around aimlessly waving their arms or palm fronds. Remarkable are Lucy Doraine's extravagant contemporary gowns, sexy historical skimpy dresses, and bizarre head wear in the biblical flashback, all created by Remigius Geyling, head set designer at the Vienna.”—
Encyclopedia.com 
