I haven't had any trouble with the ladder "rocking side to side". If you were in a strong current, there may be some movement.
After suiting up, I sit on the gunnel and backflip in to the water on the side opposite from the ladder.
When I come up from a dive, I clip a line to my BC then remove the BC. I sit (straddle) on the ladder to remove my fins, toss them into the boat and climb in. Once in the boat, I pull the BC in with the tanks.
When not in use, I store the mount under foot at the helm.
Roger