Do not make this worse by your fiancée ’adopting’ her daughter and do not make it worse by just omitting the child. Rules for immigrating adopted children are complicated, even more so when related (technically by law her sibling), and especially so in a country known for using falsified birth certificates to bring ‘children’ over. They are known to require dna test on suspect relationships - if they see a modified or late registered birth certificate or if you omit the child on the forms but later petition.
Get the DNA tests for your own records (this may even be needed for the changing of the certificates), you will prob have to do them again through the embassy for immigration, then correct the birth certificate. Personally I would suggest to delay the fiancée visa application until this is sorted out for two reasons - 1) if they are lying and it turns out that the kid isn’t hers/isn’t theirs you know before too much has gone into it and 2) so that all paperwork on her end is sorted before you start talking to us government.
Much easier to say here is situation rather than say one thing and have to correct later on. US govt isn’t too fond of the do now and ask for forgiveness later.
Hopefully she wasn’t also married to the child’s father as well?
This is going to require patience on everyone’s parts, I would recommend you also consider the CR1 instead of K1
Edit - adopting or adding a niece or nephew or sibling as their own is a common thing we see. The embassy is wise to it.