After the car heats up, the front wheels chatter when turning sharply.

Hello, definitely could be some differential clutch noise or transfer unit noise. It's hard to know without having a hands on inspection too see and hear exactly what's happening, especially with the use of a lift and the vehicle in the air. It could be as simple as fluid replacement related, or as complex as internal mechanical concerns. All Wheel Drive still syncs up all 4 wheels and allows engagement and disengagement at the necessary times; perhaps the vehicle is sensing wheel slippage as well, due too some kind of wheel sensor issue? Checking for diagnostic trouble codes would be helpful too, for "C" chassis related codes. https://repairpal.com/auto-repair-near-me