What you were told is incorrect. This is a habit of people whose parania exceeds their legal knowledge, people who often feel very strongly that they are smarter than the system and are one step away from wearing tinfoil hats so the government doesn't steal their thoughts.
The legal meaning of the term is that no rights are waived except those expressly stated in the document. Example: If I offer you $100 for your property that you claim I damaged, "without prejudice" means that my offer is just an offer of money but is not an admission of guilt.
In your case, it won't change anything. If the document waives your right to sue for neglect, then writing "without prejudice" won't change that, despite the amateurs who insist that it is important.
You can sign the document, or you don't sign it. If you don't sign it, or if you put conditions that are unacceptable to the school, then your daugher can be blocked from the trip.
In reality, signing the document won't change anything. If they are negligent, you can still sue them, and this paper will not stop it. Your signature will only prove that you knew the trip was hazardous, regardless of how you sign it.