This is a fundamental misunderstanding of how the text is supposed to work. Mining Village does not say "When you play this...", because that is the default for text on an Action card. You wouldn't claim to be able to draw 3 cards if you have a Smithy in your hand, or you deck, would you? Why not, it doesn't even come with any restriction?
For Mining Village to work as you intend, it would have to be worded:
You may trash this.
When you trash this, +$2.
Then you could play and trash it for $2, but you'd also get the $2 for Remake or similar cards. It would give you $2 when you trash it from the supply with Lurker, and when your opponent makes you trash it with Swindler (I'm not sure if the $2 on opponent's turn would do you any good normally, it's been ruled that the +1 Action from playing Caravan Guard during opponent's turn does not carry over to your turn).
Note that the ------- (a horizontal line on cards like Highway) is what separates the "on-play" text on top (which gets executed when you play the card), from the text below that can work at any time and in any place (unless restricted, like in Highway's case).
I think Tunnel is as close a card to your intended Mining Village as currently exists. It gives you a nice effect when you discard it other than during clean-up, but doesn't allow you to discard it by itself. You need to do so yourself (Cellar, Forum) or use it when opponent Militia's you. Beginning players then make the opposite error to you, they think they can just discard the Tunnel "for no reason", because why would it have that ability if you couldn't?
So generally if something is mentioned on a card in the "on-play" part, it only happens when that card gets actually played. If similar circumstances happen at some other time, the on-play effect does not 'carry over'. Trashing Mining Village any other way than by playing it will not give $2.