My personal opinion, based on processing dental gold on a fairly regular basis, is to precipitate gold first. If you precipitate palladium from a solution that bears gold, it will be difficult to eliminate the gold that is dragged down by the palladium. The salt of palladium is soluble in water, so washing is troublesome without dissolving some of the palladium.
I routinely precipitated with SO2, which has a tendency to drag down traces of palladium along with the gold. The precipitate was always a dark brown color. I accepted that as one of the problems of processing the two metals from a single solution, and refined the resulting gold a second time. That seems to eliminate the included palladium, or it is reduced to an insignificant level, if nothing else.
You may wish to see this from a different perspective if you have a solution rich in palladium and contains only traces of gold.
Remember----it your solution is relatively dilute, it's entirely possible you won't achieve precipitation of palladium. It is unlike gold in that regard.
Harold