Hello, I really cannot tell you anything specific because I do not know one very important fact about you: Are you also a former Filipino citizen who has acquired US citizenship?
Because if you are all former Filipino citizens, you can actually adopt your wife's daughter in the Philippines (where it will take a longer time, but, hopefully, it will be a less tedious, less strict and less intrusive process).
As you are all US Citizens, you can adopt your wife's daughter in the US, as well. The only problem is that their father has to be summoned by the court (this means that the father will have to be served with the adoption petition) and then, the father will need to give his consent to the adoption (this can be done by affidavit).
If the father is in the Philippines and your wife knows where he is, then, it will make more sense to adopt the children here in the Philippines as it will be easier to serve summons on the father who is also here in the Philippines. If the father's whereabouts are unknown, the petition will have to be published. Again, the costs to you if this were done in the US would be quite high.
You could also just try to have the father served with summons at his last known address and then, also allege in the petition for adoption that you have been their father. Produce all the receipts for their schooling, food allowance, medical and health insurance that you have paid for. Produce all the photos that show you and the child together, doing activities that normal fathers do with their daughters.
You also have to allege that the father has not supported the child in any way. The father has not tried to contact the child. And in fact, the father abandoned the mother and the child even before you came into the picture.
Of course, all of these things are evidentiary in nature. YOu need a lawyer. You will also need to come to the Philippines and submit yourself to the jurisdiction of the Philippine courts. You will have to bring the child because the child will be examined by a court-appointed social worker or child psychologist to determine the child's emotional and psychological well-being.
I'm sorry that I cannot give you a definite answer. Only a lawyer you hire and talk to can give you an accurate opinion. The facts you have given here are insufficient for me to give anything more specific.
The law (the Family Code) is clear in that the foreigner spouse of a Filipino citizen can adopt the child of his or her spouse. The only question you have to settle among yourselves is whether the child is willing to be adopted by you, and where it will be best to proceed with the adoption process, here in the Philippines or in the US where you all reside.
