There are several points to make here.
First is that if you are a new Zealand citizen you do not need a visa to visit the US for tourism or business purposes. You can use the Visa Waiver Program to visit for up to 90 days.
Second is that the US mostly issues a combined B1/B2 visa, which allows for both tourism and business visits, if you request either a tourism or a business visa. In any case if you say you are visiting for both tourism and business they will issue the combined visa.
Thirdly if you are on the VWP, or a combined B1/B2 visa it is perfectly OK to have some meetings with a parent company or a partner. You would need to tell the agent at the border that you are having business meetings, so that you are admitted on B1/B2 status.
You will need to be careful, because while business meetings are permitted, actual work is not. You can plan work, discuss work, review work, but not actually do work. This is important - people have been turned away at the border because they told the officer "I'm coming to do some work for my parent company" instead of "I'm coming to have some meetings with my parent company".