Technically the difference is that 'would like' communicates what you want to do and 'going to' expresses what you intend to do. So for example with 'would like' you could say "I would like to divorce you, but the law in my country doesn't allow it, so I can't." And with 'going to' you could say "I'm going to divorce you. I have been to see my solicitor, and she has explained what I must do." Of course in the real world if you ever hear the phrase "I would like to divorce you" then they probably do also mean "I'm going to divorce you"!! :-)

1) you want to divorce someone 2) you already decided, you have intension to divorce someone. You are planning to do that. So, the difference is: in the first case you only express a desire, in the second case you certainly will do that. Not an answer, because I’m not a native speaker, so, I’m not sure:)