If you turned on your AC Drove for about 10 miles and the thermostat hose broke and then you replaced the thermostat gasket and hose why would the gasket cover break again when you turn on the AC?

That sounds like coincidence to me. While the AC condenser may cause the radiator to run slightly warmer, the vehicle cooling system shold be engineered to operate well within the normal temperature range with or without the AC running. It's probably more of a function of vehicle age/miles than anything else.