Except Subutai would be leading the armies. The Khwarezm would get a reprieve as the Mongols would have to choose their new leader, but they'd be coming back with Subutai leading the vanguard against them (if not the whole army) as he did IOTL.
The Mongols are defeatable. Especially in this case, wherein the fighting is somewhat equal since the Khwarezm are somewhat like the Mongols.
The issue I have with Mongols making mistakes is that all of the Generals in the Mongol army will make mistakes since everyone who's who were in this campaign, Genghis, Tolui, Chagatai, Ogedei, Jochi, Jelme, Subutai, etc... Each of their armies should make mistakes and lose all of their separate battles.
If we make it realistic as possible, one army makes mistakes the other do not, the others just can simply cover those mistakes by taking over. Mongol mistakes would only delay the inevitable unless everyone participating the invasion makes mistakes.
I am thinking if the Shah just went for a decisive pitch battle. Use his numerical superiority over the Mongols rather hide in the walls. They had approx 5 to 1 advantage, with them having almost parity in fighting techniques, tactics. By avoiding to split, you take away Mongol generalship talent pool by making it one battle so the Shah can lead. Here one mistake can have a disastrous effect for all of the Mongols.
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