The TD visa was created by NAFTA, and is a temporary (nonimmigrant) visa issued to the spouses and unmarried children (under the age of 21) of TN visa holders.
To qualify for a TN visa, the principal applicant must be a citizen of Canada or Mexico who practices one of the professional occupations on the TN list, and be coming to the U.S. to take a job in that profession with a U.S. employer. The list of occupations is long -- professions such as accountant, architect, engineer, lawyer, librarian, dietitian, medical lab technologist, psychologist, research assistant, scientist, urban planner, and vocational counselor are among the many entries.
To qualify for a TD visa as a family member, the applicant need not be a Canadian or Mexican citizen. He or she will primarily need to show a bona fide family relationship to the TN visa holder and that he or she isn't inadmissible to the United States (such as for criminal, security, or health reasons).
A TD visa holder can remain in the United States as long as the principal TN visa holder remains in lawful status. There is no cap on the number of visas issued under this category each year. TD visa holders cannot seek employment in the United States.
To apply for a TD visa, you can either accompany the TN applicant or follow later. You would proceed directly to the U.S. border if coming from Canada, or go to a U.S. consulate if coming from Mexico, and present the following:
No: TN visa holders must intend to return to Canada or Mexico when their work is finished, and will be ineligible to adjust status. But you could always return home and then apply for a new, immigrant visa from there. Or, if you're hoping to obtain U.S. green cards for your family so that the TN holder can continue working without interruption for the same employer, then an H-1B visa might be a better option for the principal, NAFTA applicant -- or for the TD visa holder, if qualified.