I’d rather + different subject (+ past simple clause)

Question

I'm looking at this tutorial that shows the following usage:

same subject (+ base form)

I’d rather stay at home than go out tonight.

different subject (+ past simple clause):

I’d rather you stayed at home tonight.

I don't remember hearing this structure before. How common is that? I'd probably say:

I’d rather have you stay at home

Is this an equivalent and grammatically correct?

Answer 1

As the two versions are practically the same, your question is a matter of interpretation.

Let's say you are talking to me. "I’d rather you stayed at home tonight" hints that you hope the stayed at home part comes from me. You hope that I want to stay home. The form is uncommon in the US.

"I'd rather have you stay at home" says that you want my company at home. The directness makes it very American. Emphasis on rather have you, since that is the action that I prefer. Fanny Brice - I'd Rather Be Blue Over You.