Does she have to leave her husband if he does not become Muslim?

If a woman becomes Muslim and her husband is a kaafir, then
the marriage is annulled, but she may wait until the ‘iddah ends, then if
the husband becomes Muslim during that time, then she is still his wife, but
if he does not become Muslim before the ‘iddah ends, then the annulment of
the marriage becomes clear, starting from the time she became Muslim. 

Can he go back to her if he becomes Muslim after the ‘iddah
ends? 

There are two scholarly opinions concerning that. The more
correct view is that he may go back to her if she agrees, because the
Prophet (peace and blessings of Allaah be upon him) sent his daughter
back to Abu’l-‘Aas ibn al-Rabee’ several years after she became Muslim, when
he also became Muslim. 

But if she refuses then they must be separated by force by
the judge. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him)