I was at a parish recently where the priest baptized twins that had been previously baptized when born due to danger of death. I thought a person could be baptized only once, am I wrong?
You are correct. The Catechism of the Catholic Church states in paragraph 1246: “Every person not yet baptized and only such a person is able to be baptized.” [Emphasis is mine.] A person can only be validly baptized one time in their entire life. If the twins were baptized, by any person using water and the Trinitarian formula they were validly baptized at birth. If there is uncertainty regarding the baptism they could have been conditionally baptized, meaning there is an uncertainty as to the baptism at birth, “If you were not baptized, I now baptize you.” Presuming the children were validly baptized at birth, their baptism should have been recorded in the local parish where the hospital is located. That parish then remains the official location of baptism and is where the children would write for baptismal records, not the parish where you were attending.
The priest should have known better and lost the opportunity for a teaching moment. Such would have been a perfect opportunity to educate the parents, and entire parish, regarding baptism in an emergency. He could have explained that the Catechism of the Catholic Church in paragraph 1256 states: “In case of necessity, anyone, even a non-baptized person, with the required intention, can baptize, by using the Trinitarian baptismal formula.”
Based on what information you have given, the “baptism” by the priest was thus invalid and illicit.
Countenance of God 