I am surprised at the number of Captain picks. That guy's job is to get you from point A to point b, not protect you or your child from possible allergies. If your child has an allergy protect them, do not make that the job of strangers.
If the Peanut family wanted to ask their seatmates and those within a row, great, trying to inform the plane after the Capt said no is a rebuke of his decision, and they should have expected repercussions.
Can you imagine if this precedent was set?
Once that precedent is set, a captain may be forced to delay his flight departure because he is announcing whatever allergy may impact every damn passenger;