Tag question issue

[vkhu]

"You just have to poke your nose into my business, haven't you?"

Is there anything wrong with this sentence? I think the tag question should be "don't you" since the main verb of this sentence is "poke". What do you guys think?

[5jj]

The verb is 'have to' and the tag is 'don't you?'.

[Bennevis]

Since "have" is used here as a component of the modal structure "have to" and not as an auxiliary verb, in the second part of this disjunctive question we'll have to use the auxiliary verb "do" to make it right. In other words, "have" is a notional verb here.