1) Khedive Egypt (as requested), Great Britain (Interests in the port of Aden), Ottoman Empire (trying to regain control, over this area of it's empire).
If you want it as historical as possible, it should be happening between 1820 to 1870 max. Egypt was in this period capable of having such an ambitious foreign policy.
2)as you can see at the map the current division in Yemen between Houthis and government still shows the division between North and South Yemen. That division could definitely also be there in the 19th century. The ruling family for centuries in Yemen are the Qasimids. I Imagine two states, one in the North, one in the South, both ruled by a branch of that family, both claiming rule over the entire area. The Northern ruler would be named Imam (strong Zaidi brand of Islam present) and supported by Egypt, The Southern ruler Emir (or also Imam, but Zaidi's are not as strong there) and be supported by either Great Britain or the Ottoman Empire.
I hope this is satisfactory to your request for inspiration.