Upon exiting the state of ihram from Umrah during Hajj al-Tamattu', is it obligatory to enter into ihram, perform ghusl, and go to Tan'im with the intention of ihram for Hajj, or is it sufficient to perform ghusl and pray two rak'ahs in the hotel to commence the rituals of Hajj?

The Mutamatti' (pilgrim performing Mut'ah Hajj) assumes ihram for Hajj from his home in Mecca, not from Tan'im, from where one who intends 'Umrah while in Mecca assumes ihram. The Mutamatti' takes a ghusl (ritual bath) and prays two rak'ahs, if it is not a time of disliking (for prayer), then assumes ihram. The people of Mecca assume ihram for Hajj from Mecca, and for 'Umrah from the Hill (outside the Haram boundary), such as Tan'im.