Why don't you teach her an alternative behavior to do at mealtimes. You could teach her to go to mat and lie down while you are eating, or to stay out of the dining room, or even give her a stuffed kong with her dinner so she can happily eat while you eat.
If you allow her next to you while eating then make sure you're not looking at her, talking to her, touching her, and definitely never giving any food. Even if you're just looking at her to tell her no it's still attention and could be rewarding the begging behavior.