You pick the cards to discard, you discard them all in some order as a lump.
Sorry, I don't mean to belabor the point, but I'm not sure you can logically do what you're saying here. Do you discard them in some order, or as a lump?
Let me approach the issue from another direction. In this thread (
http://forum.dominionstrategy.com/index.php?topic=763.0) the question was raised whether when you play Horse Traders with only one other card in hand you should have to discard that card. Horse Traders instructs you to discard two cards. Based on the strictest interpretation of the "follow as many of the instructions on the card as you can" rule, one could argue that in this situation you would not discard the card: the instruction said to discard
two cards, which you cannot do, so you ignore the instruction. But of course the more plausible interpretation (which also happens to be the correct one), is to read "discard two cards" as two instructions: "discard one card. discard another card." You would then discard your one card because you are following the first instruction even though you cannot follow the second.
Having established this, it seems that the same logic would apply to other discard instructions. Militia tells you to discard one card at a time until you only have three cards. Minion might be different, since it says to discard your hand, but you still must logically do so in some order (and you simply cannot do multiple things in a particular order and all at the same time--you just can't). Perhaps the best card to test this would be Torturer. Say I've already discarded down to two cards, tunnel and watchtower, when another Torturer is played. Following the logic of Horse Traders, I would read the Torturer instruction as "discard one card. discard another card." It seems pretty clear then that I could discard the tunnel, reveal watchtower from my hand, and then discard watchtower. I know that's not the rule as you have declared it, but then I think you've got to explain why the same phrase "discard two cards" is interpreted differently on Torturer and Horse Traders.
One final point: Tunnel reacts "when you discard," not "after you have discarded." So I don't understand why you keep saying that you first discard everything and only then check for reactions. If Tunnel
has been discarded, technically the time has already passed in which you can reveal Tunnel.