My pup air chomps when she protests.

It's super cute, hopefully it's not a sign ;-)

We have an invisible barrier seep rating the front half of the house that the dog is allowed and the back half where she is not.

She knows the barrier and will lay down just befor crossing but if she sees you on the other side she will
Air chomp.

Aww bless her. I think it's just her way of saying "I want to be where you are"   

Aww showing off!   

Lol! Ours becomes a drama queen in protest, she'll lay down, and let out the "fine" sigh and roll her head similar to an eye roll, they do always want to be where you are for the most part :p

Sounds to like she's trying to get to the other side