I have come up with the below sentence (second sentence):

What's the problem? Would you rather I leave?

After googling I found another sentence of the same type:
"Would you rather I leave you alone?" she asked discreetly.

I assume the meaning that "instead of you I would leave". Please someone let me know if my understanding is right?

The construction of the sentence is alien for me, if possible, please elobrate more on these type of sentences to help my apprehension better.

Question

I have come up with the below sentence (second sentence):

What's the problem? Would you rather I leave?

After googling I found another sentence of the same type:
"Would you rather I leave you alone?" she asked discreetly.

I assume the meaning that "instead of you I would leave". Please someone let me know if my understanding is right?

The construction of the sentence is alien for me, if possible, please elobrate more on these type of sentences to help my apprehension better.

Answer

"Would you rather I leave" is a short way of saying "Given the choice between leaving or staying, which one do you want me to do?"

"Would you rather I leave you alone?" is a short way of saying "Given the choice between leaving you alone or staying here with you, which one do you want me to do?"

So the basic question is "Given option X or option Y, which one would you rather that I do?" but sometimes only one option is mentioned because the other option (the opposite one) is obvious.

Does that help?