It's OK to stop the motor to do this transfer, as it will save you a bit of cleanup. Proceed to take 14 quarts of fluid out, and replace them with 14 quarts of new fluid. If you want to be a purist and you have the ability, you can remove the other auxiliary cooler hose, and apply a little low-pressure air to the one that goes to the upper fitting. This will gently force the old resident ATF out through the lower hose into the drain pan. Use low-pressure air for this, and have patience.
More air means more spray which means more mess.
Reattach all the original cooler lines and hoses, drain the ATF from the new hose into the partial bottle, wipe up your dribbles, etc. Check the fluid level in the transmission. If everything went perfect, you are just a bit low, thanks to the oil you removed from the auxiliary cooler. Remember that the fluid is checked at operating temperature, engine running in park. Adjust the level as necessary.