'Hand in hand' refers to physical conjunction. People in love often walk hand in hand.
'Hand in glove' refers to a metaphorical link (often a clandestine one):
'MI5 allegedly forced Harold Wilson to resign as Prime Minister because he was believed to be hand in glove with the Communist Party.'
'The Unions are working hand in glove with the managers, and are not operating in the interests of the workforce.'
(I was toying with an example involving Qaddafi and the Scottish government, but thought that might be 'sailing a bit close to the wind'. )
- For Teachers