V-sync is the feature that is designed to prevent tearing, and generally does a good job of it. You may want to check and make sure you have v-sync on for the monitor that's running Morrowind (I can enable/disable it for each monitor on my system, IIRC). The fact that it works without the TV but not with suggests that it's specific to that monitor.
You may also try turning it on in MGE instead of the drivers, that will make sure it is applied to MW.