When I would teach ancient Africa, we'd handle Egyptian links between politics and religion both through the embodiement issue (while pointing out that the two are not separate--so not quite a theocracy) but in terms of religion and political life I used the Nile as the key pivot. The "Hymn to the Nile" is an excellent primary source to use to get at the importance of the river to all aspects of social, economic, political, and spiritual life, and to invite them to step into the mental universe of Egyptians. If they can understand the link between spirituality and the continuation of life, the politics become easier to explain.

(Using the Nile also explains why Egyptian religion and political order had such a hard time expanding beyond Egypt during the expansionist era--very useful if you get into anything regional, not that you have the available time to do that!)

This doesn't seem too complicated: the pharaoh was the literal embodiment of a deity on Earth, embodying the power of the gods and bringing it down to the commoners. The Egyptian religion gave the pharaoh his legitimacy and his raison d'etre.

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