What was the role of a division commander in the Vietnam War as it relates to his understanding of the Rules of Engagement?
The vast majority of combat engagements during the Vietnam War took place at the platoon and company level, sometimes battalion level. Jungle counterinsurgency operations simply did not allow divisional-sized combat to be a viable option. Divisions that were "on line", meaning engaging their companies and platoons on patrols and operations were led by commanders removed by nature of their position from anything like front line fighting.
My take on their understanding of the Rules of Engagement is that they were much more likely to have their hands tied by Corps Commanders and institutional policies than the small unit commanders. That is to say division commanders were more of a hindrance to a unit's combat effectiveness than a help. While there were exceptions of course, and it varied according to leadership style and initiative of the commanders themselves, the division commanders in Vietnam were, I think, farther removed from combat realities than in most wars.
As a result, officers at the small unit level were sometimes only as effective as their methods at getting around the rules of engagement, or at observing the spirit of those rules rather than the letter. Jungle combat conditions allowed this more easily too.