There were lots of short-lived nations that were an attempt at a unified Arab nation-state. The aforementioned UAR, United Arab States, Federation of Arab Republics, and a few more. The United Arab Emirates is actually a successful example of such a unification, although obviously much smaller in scale than the others, and it doesn't really have the ultimate goal of total Arab unification.
So, start off with Syria not having a coup, and remaining in the UAR. Eventually, Iraq joins the UAR (planned, historically, but ended up not happening). This is a bit more likely ITTL, since the UAR is still intact, rather than just being Egypt with a different name. So, that's Egypt, Syria, and Iraq. Saladin also had western Saudi Arabia and Yemen. Yemen (or at least part of it) is easy; the UAR was in a sort of federation with North Yemen, which dissolved after Syria broke away from the UAR in the early 60s. With no Syria coup, North Yemen stays in, and and eventually the UAS confederation truly integrates.
At this point, you more or less have Saladin's territory, except for South Yemen and Hedjaz. I doubt you could get Hedjaz unless all of Saudi Arabia decides to join the UAR/UAS, which I don't see happening. South Yemen will probably join in eventually, similarly to how it rejoined North Yemen in the late 80s.
Hussein gains power sometime in the early 80s, truly integrates the nation, and possibly leads directly to the annexation of South Yemen (through peaceful means). He's lauded across the UAR as a great leader, and the west loves him for bringing a pro-Western stability to the important region.
A better starting point might be the Federation of Arab Republics, because it was closer to Saddam's rise to power, but I don't think other Arab nations had much of an interest in joining it. Maybe it becomes a bit more successful (similar to the UAR proposal), and so Hussein's Iraq decides to join in. This would give much more credit to Hussein, since he was the one that actually brought Iraq into the federation, and since he's already in power in Iraq, it'd be easier for him to take over in the Federation.