Based solely on the first post...more often than not shooting left or shooting low is a problem with the shooter. Shooting left is generally poor trigger control, and it makes sense that a short and light single action trigger like a 1911 would mask that problem while a 'double action' pull like a Glock would show it.
That said if you are shooting consistent groups, even under extremely slow precision firing, you might just need to bump the rear site to the right a little bit. I have three Glocks, each of which I have plenty of rounds through, and I have extensively fired a fourth as well. I had to bump the rear sites to the right on every single one...some more than others. And not due to trigger control, trust me.
SOOO it is probably trigger control...but not necessarily.
Edit: I strongly, strongly advise against a lightened trigger, especially a 2lb trigger, for a defensive firearm. I also strong advise against lightening the trigger instead of learning how to pull it without twisting the gun off target. A stock Glock trigger should be something you are more than capable of running proficiently.