1980, Iraq invades Iran same as OTL, most of Arab world backs Iraq. Egypt is ignored but strengthen ties with Europe by selling more oil.
Why a constitutional monarchy when the monarchy hadn't existed for over 20 years and IIRC had no real support? It isn't like the Hashemites where all the monarchy of Iraq and Jordan were related.
I suppose if you're a hardcore Pharaonist you might want a monarchy so you could have a Pharaoh, but anything like that would never be in the majority of Pharaonists at that point. And as I said, taking over and annexing Libya clearly means you have some pan-Arab goals.