Clarification of the recognition of foreign adoption

So Angie (travel buddy) brought to my attention that because we both traveled we aren't doing a "re-adopt". We are just going to court to let the judge see our paperwork and say "yep, it's legal, an adoption did occur...now go get a birth certificate." Sorry I used the wrong terminology...thanks Angie : ) This however was still going to cost us 500.00 for the lawyer to fill out and file that paperwork. I believe that they will hand us her new birth certificate in court but I'm not hundred percent sure. I know we are paying the filing fee and the birth certificate fee so we'll see when we get there.