What if Jordanian king Hussein suffered the fate of his cousin, Faisal of Iraq, and was toppled by a military coup the same year (1958) that established a republic? Would keeping Suleiman Nabulsi, who pushed for closer ties with Nasserist Egypt, as prime minister (he was removed in 1957 after being in government for a few months) help?

Would this hypothetical Jordanian Republic join Nasser's United Arab Republic? Assuming the UAR doesn't fall apart after a few years, would Nasser still try to fight a war with Israel (which would likely be terrified now that it's surrounded by a single state) in 1967 or so, or would he instead spend the rest of his tenure consolidating it?​
I wonder if Israel might get involved in restoring the monarchy.
I'm more curious if the ongoing Lebanon crisis would be affected in any way. Was there ever a chance for the US to just abandon the place to the UAR with the view that "well, they'll take everything from Egypt to Iraq (minus Israel) anyway, might as well let it go and keep them on our side"?