Our shop's pool work is done at a local recreation center, which means hauling gear to and from the site. Every instructor I know does things the same way. Any professionals working that day show up at the shop and work together to load the van and then unload it at the site. They then begin working together to do what has to be done to distribute materials at the site. Once students arrive, the instructor(s) begin working with the students while the DMs do whatever else needs to be done before assisting students with gear setup, etc. After class work is done, the professionals all work together to gather material to be moved back to the van. Each instructor divvies up that work a little differently. For example, I will have the DM demonstrate how to wash the gear and then supervise that process because I am tired of instructing at that point and would prefer to haul gear while that is going on.
I think the grunt work that does on before and after the instructor is working with the students needs to be shared as much as possible. In many cases, though, the grunt work will fall to the DM. For example, after the OW dives, the instructor needs to debrief, log dives, sign logbooks, sign papers, etc. It would be silly to have the DM standing around watching the whole time that is going on, so a lot of grunt work will naturally have to be done by the DM.