To accomplish an adoption of stepchildren, your wife must file suit and give notice to the mother of the child. It is possible that the father would be agreeable, and if he is, he can sign an affidavit to that effect. The judge may decide that an attorney should be appointed to represent the child (attorney ad litem) in a step-parent adoption circumstance. If so, you can expect to pay that attorney as well.
Call 214-373-9292 or contact us to discuss your concerns.