Is it possible for the spouse/child to apply for a J-2 visa after the J-1 principal has already traveled?
Yes, subject to fulfillment of certain rules. The spouse/child must complete SEVIS generated Form DS 2019 (approved by the sponsor), show proof that the principal applicant is maintaining his/her J visa status and submit copy of the J-1’s (principal applicant’s) visa, proof of relationship to the principal applicant, and proof of sufficient money to cover all expenses in the United States.