The OP has already said that she regrets her handling of the incident.
I think that the new person was quite clueless and also rather rude to ask her a question during lunch, and to keep talking after she first said "stop." It sounds like the new employee is rather impetuous, and has a one track mind.
When I was teaching our only real break was a half hour lunch. When the kids were off at a special we were either correcting papers, preparing lessons, or contacting parents - all done at warp speed. One clueless secretary had to be told by the principal not to tell parents that we would be able to return a call during our lunch, since we barely had time to eat.
The half hour was not a whole half hour to eat, either, because in that time period we had to either buy or heat up our own lunch, walk to the staff room or our classroom to eat, and use the restroom. Absolutely we had to be back on the minute to collect the children again, because they would be lined up and waiting. Being kids, if they waited too long they tended to find unacceptable fun things to do in the interim.