Congratulations on your new puppy! I've had Max for almost 4 years and I still wake up thinking how much I love him.
When you have her sectioned off in the kitchen, can she see you? Usually if they can see you, they are okay. She probably wants to be underfoot at all times. I trained my boys to know that when the humans sit at the table to eat, the doggies have to do their own thing. Ignore the crying and she will eventually stop. If you give in once, she will know that crying gets her what she wants.
ETA: my boys have beds under the table and that is where they go when we are eating.
Good luck and enjoy!