Yes, you're right. But when we enter the picture, they will unite against us - even if only temporarily...
Saudi Arabia and Egypt would never fight us, even if just temporarily. First of all they'd get their towells handed to them handily, and they know it. Secondly, as I mentioned, they far prefer to sit back and watch us (and Israel) destroy their regional rival (Iran). And lastly, they have too much to lose financially: Egypt gets $2 billion/yr courtesy of the U.S. taxpayer, and Saudi Arabia lives off American oil revenue. ...and they have major U.S. stock/bond holdings.
Sorry old chap, the Arabs will NOT unite against us with Iran as their ally. They are terrified of where Iran is going and will possibly talk alliance but never join in and will covertly do anything they can to help us beat Iran.