-The two-year home residency requirement or two-year repeat participation bar does not affect your child J-2 visa application in China based on your spouse's J-1 status. So, your child may apply for the J-2 visa to come back.
我们是否可以自己去移民局给孩子办这个J2签证延期呢?
-No. The sponsor/university needs to issue a new DS 2019 to your child for J-2 extension or J-2 visa application, and also put this information into SEVIS.