There are two reasons this isn't working: your expectations and your technique. It's unrealistic to expect a child your daughter's age to be able to sit still at a dinner table for more than a few minutes. From her perspective, the world is simply too exciting a place; it needs to be explored.
The way she explores that world is through play. This is the "work" of childhood. From her perspective, the best toy in her world is you. She's figured out a way to turn mealtime into a game with you that allows her to get both food and attention.
Changing these habits will take a bit of time. The first step is for you to recognize that it will be a few years before she'll be able to amuse herself at a dinner table without help. Start by aiming for three minutes, then five, and so forth. This will help you avoid turning mealtime into a battle of wills.
Depending upon her size, put her in a high chair or a child's booster seat. Some children feel much more secure if their feet can rest on something instead of dangle. Once she's too big for the booster seat, you may want to try a small table and chair that you put next to the adults' table so that she can eat with you and get your attention while staying comfortable.
Put one or two of her favorite small toys on the tray or on the table so that she can play during her meal. Pay extra attention to her while she's eating. (Your own dinner will wait.) If she's getting antsy after a few bites, lift her out of the chair and go for a one-minute walk around the room before returning to the meal. When she's through, clean her up and let her go back to playing while you eat your dinner. She'll quickly learn that she'll get more attention from you at mealtime by staying in her chair.
