Like Lark said, if you don't want her to beg don't reward the behavior by giving her anything when she begs.
As for feeding dogs people food. There are some foods that people eat that are toxic for dogs. There are some folks who say you should never give dogs people food. Personally, I share some of what I eat with BG. I don't like pizza crust and he does so I share, that sort of thing.
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