This all can be very confusing and difficult to wade through. The nurse practice act in each state determines what is required to become a registered nurse, LPN, or LVN in that particular state. You should be able to find the nurse practice act for your state here:
You might be subject to the policies of the institution where you do your clinical rotation. That can be found in the policy manual or employee handbook.
A couple of questions come to mind. What is the policy of the educational institution where you are enrolled? Is this institution allowed to require drug testing because of your past history?
Since I'm not an attorney, I can't answer those questions. You might want to discuss this with an attorney dealing with labor laws and/or an attorney familiar with nursing issues.
Here is a link to a brochure about the Americans with Disabilities Act. It does discuss work and education related issues.
PRIVATE EDUCATIONAL, HEALTH CARE, AND OTHER FACILITIES
It does appear that many nursing programs require a background check and drug screening because the institution where clinical rotations take place require background check and drug screening for prospective employment. Here in Ohio, fingerprints and background checks are required for anyone applying for a nursing license.
The question I have is, do you have a criminal record as a result of your chemical dependency? If not, disclosure may not be required. Again, the legality is something to take up with an attorney. The American Association of Nurse Attorneys may be a useful resource. http://www.taana.org/
Good luck and congrats on your recovery!