I did not include the stock cooler when I hooked up my aftermarket cooler. I was monitoring my Transmission Fluid Temperature (TFT) before the cooler and it would stay around 180*-200*. With just the aftermarket cooler, stays around 140*-160*. Good to go.
This is another of those fiercely debated issues. You'll find the same discussions on other vehicle message boards too. There are many arguments to the "in-line" configuration.
Some feel it's best to put the new cooler on the return line. That way, the stock cooler drops the temperature some, then the aftermarket cooler will drop it even more. The temps I got with just the aftermarket cooler show that you don't need to pre-cool it. A decent aftermarket cooler will do the job.
Some feel it's best to put the new cooler on the supply line. The thought here is that the stock cooler will bring the TFT closer to "the ideal" temp of 180*. Instead of supplying the transmission with 160* fluid, the stock cooler would raise it to 180*. I don't get that either. The transmission will do that, and then some. No need to pre-heat it.
There's also the belief that the stock cooler (being attached to the radiator) will pre-heat the fluid in the winter time. But in those freezing temperatures, the thermostat will be closed or just barely open. The coolant in the radiator won't be hot enough to pre-heat anything. Again, the transmission will heat up the fluid itself.
It's your call. If I had to do it all over again, I'd still go with just the aftermarket cooler. Nothing else.