The only reason I can think of that might prevent you from being present during the administrator's investigation is his concern that you might influence your daughter's answers / accusations. Sometimes children say (in front of parents) what they think their parents want them to say, so that might be basis for his decision to question your daughter out of your presence.
With that said, if you are uncomfortable with his decision to exclude you, then you might consider asking that another staff member question your daughter independently, as well, to counteract any influence the principal may have had on your daughter's comments (i.e. the school counselor, her teacher, etc.). Alternatively, your school district probably has a grievance process you can utilize to complain about the way in which the principal is handling the situation. Check the district's website for information on parent grievances/complaints.
Ask the school to set up the speaker phone capability in the office before the child comes in so that you can silently -- SILENTLY AND WITHOUT PARTICIPATING -- "observe" by listening. The school is entitled to take a statement from the child that is not influenced by your participation, expressions, gestures, etc., but there should be no reason that you cannot listen in silently (and take notes or even tape record) without the child being aware that the speaker is on.
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This situation is now governed by NJ's anti-bullying statute which "require[s] each school district to post its anti-bullying policy on its website and distribute it annually to parents or guardians of students enrolled in the district." NJ 18A:37-13.12.d. You should check your local District's website to see if your local Principal is following that procedure.
Furthermore, under NJ statute18A:37-15.3., "Adoption of policy concerning harassment, intimidating or bullying by each school district, [e]ach school district shall adopt a policy prohibiting harassment, intimidation or bullying on school property, at a school-sponsored function or on a school bus. You can read the statute yourself (as it is straight forward) at the link noted below.
You could ask for the accommodations noted by other attorneys, but they don't have to do so.