Grace doesn’t want to move to New York because (she thinks) if she were to live there, she wouldn’t be able to see her parents very often.

because引导原因状语从句，she thinks是插入语，去掉插入语，这个句子结构就更清晰了，if she were to live there是原因状语从句中的一个虚拟条件句。并非您所说的think后面接if还是接that区别的问题。