If you are holding a J-1 visa, you would be subject to two-year, home-country physical presence requirement, if you participated in any of the following types of programs:
Generally, your program sponsor should inform you whether you are subject to this requirement. If you are unsure or wish to receive a confirmation, you may request an advisory opinion from the U.S Department of State.
You may also take a survey at the U.S. Department of State's web site, to see whether you are subject to the two-year, home-country physical presence requirement. However, you should know that this survey is informal. If you wish a definite answer, request an advisory opinion.
If you are subject to two-year, home-country physical presence requirement, the same requirement would equally apply to your family members, who are holding J-2 visas.