In the case of Peruvian birth certificates, we found that there had to be an extra stamp which qualified the birth certificate for "external use." This seems really strange, because like you said it's the same birth cert that we used for her K-1 and it was approved... but whatever. I strongly recommend that you NOT simply get a "letter that states that the birth certificate is official." We had to pay for a whole new one: New certificate, new translation, and then the stamp for "external use."
I called USCIS and after 3 calls and 5 hours on hold, finally got hold of an officer. He was very nice, but extremely unhelpful, as he only said "Call the Peruvian government and ask what you should send." (The "Peruvian government"?!!? Yeah I just have that right here on my speed dial...) My advice: Don't call USCIS. They're kind, but very useless.
We WILL be including as much secondary evidence as we can, just to be safe. This would include baptismal certificates ONLY if you were baptized within 2 months of birth (in our case, she wasn't). Anyway, we're going to put together the hospital records, a copy of her voter card, and a couple of affidavits if we can.* Best of luck!
Thalia.Fanchiang reacted to Lemonslice in Others approved before