USA-New Zealand export/import business
As far as I see there are several scenarios that could work for that type of business. First of all I would break this business into two "sub-businesses": US exporting business, and NZ importing business.
Scenario #1: US exporting business is organized as an LLC (choice of state could vary, with TN being a strong candidate due to the fact that your sister lives there and operated from there) and owned solely by your sister. NZ import business is organized in New Zealand (as you already have it done) and owned solely by you.
This scenario presents a strong separation between the businesses, and makes it easier for each of you to handle the question of taxation (since you will only be taxed each in her own country). The downside of this scenario is the fact that you wil need to come up with a solid schema on how the profits and the risks from the combined enterprise would be shared by both entities.
Scenario #2: US export business is organized as an LLC and owned by both you and your sister equally. NZ import business is organized in New Zealand and is also owned by your and your sister equally.
This scenario removes the awkwardness of you two running separate businesses, however it contains a complication of international taxation. Not being an accountant and not being familiar with how the profit earned in New Zealand is taxed in the US and vice versa I will not be able to advise on a course of action for this scenario, so I recommend you to consult a professional accountant before going that way.
Scenario #3: register the NZ company in the US as a foreign entity. This scenario is somewhat similar to #2, but in a way more complicated (foreign qualification of overseas entities is beyond the scope of this question, but in general its simply easier to form a US LLC instead).
The choice of state is another question, and it depends on the type of activity in the US. If the business would be physically located in Tennessee and would have local expenses it could make sense to register it there instead of Delaware or any other state for that matter. A professional business attorney would be able to advise further on a choice of state, based on the analysis of your specific situation.
I hope my answer was helpful for you to understand things a bit better.