Pull data from one DB Server to another DB server
You have a few options.


Copy data in the correct order. Find the parent child relationships and insert data to the parent tables first.
Drop or disable the constraints, insert the data, then recreate or re-enable the constraints.
Use a tool like Redgate SQL Data Compare, which will identify the heirachy and copy data in the correct order for you. 


If you want to know more about how to find foreign key constraints there is a great post here