Your daughter's rhythmic head swinging is unlikely to be a tic. There are several reasons for this. One is that age 3 would be an extremely young age for a child to develop a tic. Most children do not manifest tic's before 6 or 7 years of age. Another is that tic's are not continous though they may be continual. That is they may happen with great frequency, but they always have some pauses.
Another characteristic of tics is that they evolve and change over time. They do not remain absolutely the same over many years.
Tics are also typically sudden and jerking, paroxysmal, explosive. They are not rhythmic.
Finally, the clumsiness and falls worry me that this is more than a tic.
I hope you can get an evaluation for her. Quix
Could be tourettes.
Quite often people with conditions like tourettes have overlapping symptoms with other conditions such as dyspraxia, aspergers adhd (which you mention) etc which often have balance problems and clumsiness.
Quite apart from my ongoing twitches, I have noticed on video that I have a head mannerism of jerking my head to one side at certain points when I am speaking, no reason why, it's just something I do
Has your daughter been evaluated at a major academic pediatric center? The first neurologist blew you off. He didn't know so he dismissed you. I don't buy a "tic" lasting 10 years. The concept of this being a "habit" , to me is laughable. I am concerned that she might have a problem in the part of her brain responsible for balance and coordination in space, the cerebellum. Do her eyes jiggle or jerk?
I believe she needs a THOROUGH pediatric neurology evaluation which might include motor/balance testing, neuropsych testing (because of the ADHD) and a neuro-ophthalmologic evaluation, possibly genetics. If you are in the US look at some of the major university medical centers and arrange for your daughter to be evaluated properly. Examples of these centers would be (out of hundreds) Boston Childrens, Cleveland Clinic, Duke, Vanderbilt, University of Chicago, UCLA, ---I shouldn't have even started listing them. There are so many really good centers.
She deserves an answer. I hope you can find help. If you do get an appointment take all of her medical records and copies of her films with you.
Good luck, Quix