The Automatic transmission breather tube is on the drivers side of the vehicle and is under the air filter box under the hood, it often reaches up near the battery tray.
The location of the transmission vent on a Cougar depends on the year it was made. On the 1999 to 2002 models it is located on the driver's side of the engine.
If it's a vent hose it doesn't go anywhere.
There is no transmission vacuum hose. That is a vent hose.
it should be under the passenger side dash by the heat vent
On my 97 SC1, the vent is a tube between battery and firewall. Not sure if the same on the SC2.
I noticed thet you selected stalling as your problem. The emission code will not cause a car to stall. I think you need to clean the Mass Air Flow sensor and run a cleaner through the air intake.
There is a redesigned transmission vent that should fix this problem.
It depends on the year, for Cougars made from '99 till '02, the Automatic Transmission Breather hose is located on the drivers side of the engine, underneath the battery tray.
a Blocked heater core
On the top of the transmission.
Assuming your temperature selector is not on "cold", the heater core is likely bad
on the transmission