have to do sth结构中，have不是操作词，倒装时必须借助助动词do:

Do you have to leave tomorrow?

have got to do sth 结构中，have got实际是现在完成时形式，have是助动词，为操作词。倒装时则直接倒装操作词have:

Have you got to leave tomorrow?

原句本身就有操作词，提问时再加其他操作词必为错误：

Do/Will you have got to leave tomorrow? 错误！！！

要知道have在什么情况下为操作词，什么情况下不是。这是基本的。