It depends.
While some countries take to naming their head-of state's relatives a certain way, this is not the case for all countries as it is most often just a nation's own way of specifically identifying the members of their head-of-state's immediate family. The reasons they are called such vary from country to country, so therefore it completely depends on the country of which you are talking about.
Either the cabinet minister has to resign (if the cabinet still supports the Prime Minister), or if the cabinet no longer supports the Prime Minister the Prime Minister has to resign (resulting in a party election) or the Prime Minister can call a general election.
Yes in Russia.
Prime Minister.A prime minister
Mohammed Najib - the Malaysian Prime Minister.
He is called the Prime Minister.
PM (Prime Minister)
Prime minister, in norwegian: Statsminister.
The head of the federal government in Canada is called a Prime Minister. There is no other term used.
Margaret Hilda Thatcher, because she had a Husband.
Prime Minister, currently David Cameron
He and his husband both support same-sex marriage. He is the second prime minister of a country to marry someone of the same sex while in office. The first was the former prime minister of Iceland.
The head of the Government is the Prime Minister. The name of the current Prime Minister David Cameron, who succeeded Gordon Brown in 2010.