IPC states no direct connections to any device that provides sterile goods (utensils) for the use of human consumption be directly tied to any source that contains contaminates. This code is laxed in some states but the core reason for Air Gaps stands unmatched in protection of the reversal of contaminates. High looping does not protect the reversal of flow; it's a shortcut allowed but does not fully protect. The first attempt with a plunger to unclog a kitchen sink drain will push that sewage into the dishwasher. Granite installers are notorious for avoiding drilling holes for them. They just say "high loop it" and it will be okay. Any plumber who respects their license should know to think outside the code book when this type of situation is presented when you replace a dishwasher or garbage disposal. You take your reputation and license into risk when you "high loop it" in an area that enforces that code regarding Air Gaps. As long as there is a connection to the waste system BELOW the flood rim level of the fixture it serves, it is susceptible to not protect the device used in producing sterile goods. The situation is not uncommon; clog kitchen sink with wastewater in the dishwasher is fairly common in plumbing forums across the www.

How are you venting it?

Cut the trap off at the female at the wall. Cut slots in the remaining female with a Rotozip, then chisel the pieces off. Do not break the male in the wall or you’re in trouble. With a clean male stub out of the wall, prime and glue a connector, a 2 1/2” piece of 1 1/2” PVC, and a new trap with a 1 1/2” piece of PVC primed and glued long enough to reach the drain.

In my experience, the drain flange assembly, when properly attached to the subfloor, adequately stabilizes the P-trap. It's like your sink: there's a flange from the drain that the top of the P-trap is attached to, and there is the drain line that the bottom end of the P-trap is attached to, but the P-trap itself does not get any extra support. A shower P-trap assembly is typically glued and not removable, so it should be even more solid than a sink assembly. Why can your flange move around? Is there another part that attaches to the flange that will be secured later, or is this supposed to be a finished plumbing job? A picture or two of what this looks like right now might help.