Can we use them interchangeably or there are situations where only one of them is correct?
The difference is that You do have to is emphasising the obligation, usually in contrast with a suggestion (or statement, or speculation, or even an assumption in a question) that you do not have to.
I don't have to, do I? Yes, you do have to.
My researches suggest that I don't have to do this. I'm sorry, you do have to.
Do I have to do X first, or Y? You have to do X. (You do have to do X would sound odd).
You do have to is odd if there is no contrary suggestion already in the discourse.