When creating a view how do I separate one column into two depending on a foreign key value?
you need to use CASE construction in the query SELECT list:

SELECT
   CASE 
      WHEN aty.address_type_id IN (1,3) THEN a.Address1 ELSE NULL END as mail_address,
   CASE 
      WHEN aty.address_type_id =2 THEN a.Address1 ELSE NULL END as physical_address
....
FROM ...