First, I don't have access to engineering specs, so can't answer with absolute confidence, so this is largely opinion mixed with theory, but as to whether to route to stock cooler first, then auxiliary cooler or vice versa, I believe it would depend on whether the stock cooler is co-located in the radiator. If so, "cooler" may be a misleading description of what the device is intended to do.
The question really is whether the transmission, normally, runs hotter than 200 degrees, and I believe that without a cooler of some sort, most automatic transmissions will run hotter than that. If so, running transmission fluid through the cooler located in the radiator will generally bring the temperature down to around 200 to 220 degrees. It is a "cooler" only to that extent. A transmission intended to operate at that temperature would not want a regular influx of cold fluids.
Stock cooler tanks co-located with the radiator are more a temperature stabilizer than a cooler, and to some extent they do warm fluid faster on cold mornings, which is a good thing. If the transmission is working normally and the fluid is not cooking off or burning, then the system is working normally and an extra cooler is not needed. If your transmission needs to run at a stable temperature in the low 200's, adding a cooler after the stock cooler would defeat the engineer's intentions.
But if the transmission is running a bit hot, and needs to stay in the low 200's, putting the extra cooler first might help bring the temperatures down quickly without taxing the radiator's power to cool the fluid down to normal operating temperatures. In other words, with a hot radiator the stock transmission cooler located in the radiator will have a high threshold and have difficulty dropping fluid temperatures to the intended level. Cooling efficiency decreases when the temperature of the fluid and the temperature of the "cooler" are close together. In this situation it would help to have an auxiliary cooler, but if you still want to regulate the fluid temperature, putting the auxiliary cooler after the stock one would leave you with cooled but unregulated fluids. You would never really know what temperature fluid you were returning to the transmission.
So, I would agree that it makes sense, if you must, to plumb the auxiliary cooler between transmission and radiator, and let the radiator regulate the temperature of the fluid being returned to the transmission, rather than the other way around. If, however, your stock cooler is a stand alone passive cooler, adding an auxiliary cooler only increases cooling capacity, and whether one comes before the other would be moot.