Q: 2003 Yukon stalls going down hill and at abrupt stops.

Hopefully, the two stalling scenarios have only one cause. Among the possibilities are a faulty torque converter lock up. You might be able to detect that with a sophisticated scan tool, such as the Tech 2. If the level of fuel in the fuel tank is low, or there is some strange debris "situation" in the tank, the sudden stop, or the downhill orientation might be blocking the fuel supply. This has happened with filters during sudden stops. If the filter has never been changed, that is certainly a harmless stratagem, especially as filters should eventually be changed. Overall, to rule out fuel supply as the issue, you can tee in a fuel pressure gauge and just simply monitor the pressure while driving during these incidents and see if pressure falls off precipitously during a sudden stop. If it doesn’t then the issue is not fuel and is probably electrical or transmission related. There have been cases where a vehicle stalls every time a left turn (for example) is made and the fault is traced to movement in a wire harness that momentarily interrupts a key circuit (a wire has a break in it). Your issue is resolvable though and I would suggest that you request a stalling diagnostic. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.