Will my USA born child get HHR and National ID after I finish my 1-yr. TARC?

So we are trying to get a national ID and HHR for my wife through her taiwanese parents. She had an expired TW passport when we had our kids. Now we are planning to go back to taiwan for 1yr so she can get her TARC/HHR. After her 1yr is complete, would the kids be able to get HHR right away? I have read someone else mentioning their kids would have to stay another yr for their HHR, making that 2 full yrs instead of 1…

I am not sure what to do, but i believe my kids and myself would need a visitor visa to enter TW then convert all 3 visas to ARC once my wife gets her TARC?