J-1 to J-2
You can change from J-1 to J-2 without leaving the US if you apply before your current J-1 expires irrespective of the 2-year HRR condition, if any. You need to file I-539 with supporting documents.
If your wife\'s program has 2-year HRR clause and if you opt for J-2, then you too are subject to the 2-year HRR. However you (and your wife/family) will need two waivers or two fulfilments if BOTH (your current J-1 and future J-2) programs have 2-year HRR clauses on each befoe you can get the US permanent residency (immigration visa/status) anytime in future.
Best wishes,
Jigesh
Disclaimer: Personal non-legal point of view only.