The majority of scholars are of the view that a Muslim who performs `Umrah during the months of Hajj, then returns to his or her family before traveling back again for Hajj does not have to offer sacrifice because he or she is not considered to be doing tamattu`.
In Majmu` Fatawa Ibn Baz [The Complete Fatwas of Sheikh Ibn Baz], the former mufti of Saudi Arabia, states,
If a person performs `Umrah in Shawwal then goes back to his family, then comes to do Hajj on its own, the majority of scholars are of the view that he is not doing tamattu` and he does not have to offer a sacrifice, because he went back to his family then he came back to do Hajj on its own. This is the view that was narrated from `Umar ibn Al-Khattab and his son Abdullah (may Allah be pleased with them both), and it is the view of the majority of scholars.
On the other hand, it was narrated from Ibn `Abbas that the pilgrim in this case is doing tamattu`, and that he does have to offer a sacrifice, because he combined `Umrah and Hajj in the months of Hajj in the same year.
But the majority of scholars say that if he goes back to his family — and some of them say that even if he travels a short distance — then comes back for Hajj on its own, then he is not doing tamattu`.
It seems, and Allah knows best, that the most correct view is that which was narrated from `Umar and his son Abdullah (may Allah be pleased with them both): If a Muslim goes back to his family, then he is not doing tamattu`, and he does not have to offer a sacrifice. But for the one who came to do Hajj and did `Umrah and then stayed in Jeddah or At-Ta’if, and he is not one of their people, then he entered ihram (state of consecration), this person is doing tamattu`, and the fact that he went to At-Ta’if or Jeddah or Madinah does not mean that he is no longer doing tamattu`, because he came to perform them (`Umrah and Hajj) together, and he went to Jeddah or At-Ta’if only for a reason. The same applies to one who goes to visit Madinah — this does not mean that he is no longer doing tamattu` according to the most obvious and most correct view. So he has to offer the sacrifice of tamattu` and do Sa`i for Hajj just as he did Sa`i for `Umrah.