How to address the question tag after gotta

Josh,
you wrote:

<<Do you use "don't you" for every tag situatiion? Why don't you use "haven't you"?>>

I do use "haven't you", but only when the sentence contains 'have':
"You've been to England, haven't you?"
I don't use it with 'have' as a full verb meaning 'to possess':
*"You have a car, haven't you?"
Instead, I would use "don't you" or "right" for this.

'gotta' is short for 'have got to' where 'have' is an auxiliary verb and 'got' is a past participle. In standard English questions are formed by inverting 'have' and the subject

Have you got to go?

and negatives are formed by putting 'not' between 'have' and 'got'

You haven't got to go

If you use 'don't' in a tag question for a sentence with 'gotta' do you also use 'don't' in negatives with 'gotta' ?

you don't gotta go or you don't got to go

and 'do' in questions with 'gotta'?

do you gotta go? or do you got to go?

in effect, has 'got' become a separate verb for you meaning 'have' or 'possess' and distinct from 'get'?

<I do use "haven't you", but only when the sentence contains 'have'>

Why don't you use "don't you" there also? If you use it here "You gotta go, don't you" (where it is omitted), why not here "You have to go, don't you"?