the priest would not necessarily repeat the Baptism conditionally, but just do the other ceremonies that normally surround Baptism, such as Stubborn mentioned: vows, candles, exorcism, etc…  I don't think he would repeat the actual Baptism itself, unless there was reason to doubt it was done correctly.

My other thought is, have the parents asked the priest for advice?  

I believe the parents are well informed on how to baptise validly. It is more a situation like parentsfortruth describes. I do not know the answer to your question. But thank you for asking. An important question.