If I understand you correctly, you are saying the court has awarded you temporary custody. Usually, that is done via a 3rd Party/Nonparental custody action. If that has been started, finish it.
If it has NOT been started, you need to start it.
As to adoption, you cannot adopt unless BOTH parents relinquish their rights, or have their rights terminated by the courts. But that is complicated and regardless, I suggest you consult a local attorney.