Some hopefully-helpful info:
There is no need to pump anything out of the cooler line before dropping the pan. The purpose of pumping oil out of the cooler line is to flush the converter. The pump picks up fluid from the sump (through the flat sump filter), then pumps it out to the hydraulic system (including the converter). When sitting in Park or Neutral, fluid from the converter is sent to the cooler. So if you pump oil out the cooler line (before dropping the pan), yes, you are pumping old oil out of the converter, but you are merely replacing it with more old oil, that the pump is pulling out of the pan. So the net effect is, you are just draining the pan through the cooler line (which, if you run it dry, is NOT a good thing). So just drop the pan first; you will accomplish the same result with no risk of damage. If you are adding oil through the filler tube (while pumping oil out the cooler line, BEFORE dropping the pan), then you are just mixing good oil with bad oil in the pan (kinda wasteful I think).
So drop the pan and change the filters first. Measure how much oil you drained out. Then reinstall the pan, fill it with the same amount of fresh fluid as you drained out (see below for more details), and THEN do the cooler line pump-out if you want to. You will then be feeding only good fresh oil into the converter. It doesn't matter which line you disconnect, or where you disconnect it. You just need to know which way the oil is flowing, so you know which side to plug, and which end to stick in your bucket. The oil gets pumped out of the upper line on the transmission, and comes back through the lower line on the trans. Always plug the "downstream" side when you do the disconnect, to prevent the pump from sucking air through the return line.
The converter holds two gallons of oil. If you let the trans drain (with the pan off, and the spin-on filter removed) for several hours, you can usually get half of the old oil in the converter to drain out (in which case, you should get about 11 quarts of old oil drained out, for a stock pan). Then, you should only need to pump out about a gallon of oil through the cooler line, in order to flush the converter. If you do a "quick change" on the pan (and don't allow time for the converter to drain out), you might have to pump out two gallons through the cooler line to get it flushed. Make sure you add the same amount of fresh oil to the trans as you pump out of the line.
You will ultimately use the SAME amount of fresh fluid either way; I just want you to be aware of how much you might need to pump out. If you let the converter drain down all the way (i. e you get 11 quarts out of the pan), then when you fire it up it will draw one gallon of oil out of the pan just to refill the converter (before you start getting any significant flow out the cooler line). It usually takes about 7 quarts to fill a stock pan, so if you fill it with 11 quarts (the amount you drained out), it will be WAY overfilled, but this will quickly disappear once the pump pulls out that gallon of oil to refill the converter (and you will then be OK on oil level). But if you had only dumped in 7 quarts, fired it up, and waited for oil to come out the cooler line, you would be down to only 3 quarts left in the pan (getting close to sucking air!) before the converter refilled.
So, bottom line: Add the same amount of oil back into the pan, as you drained out of the pan.