how does the government control personal relationships?

Yes, ordinarily they would be vaporized before you can say Big Brother!The irony is that O'Brien knew about the relationship for some time, he just found Winston interesting. The Party controlled relationships by strictly deciding who you could and could not talk to. Katherine, Winston's first wife, was matched with him precisely because the loathed each other. All the Ministry of Love was interested in was an offspring to continue the population.