So does Throne Room lose track of Mining Village, or not?
It has nothing to do with losing track. Mining Village says "If you do, +$2." So you play it once with TR, then trash it for $2, then try to trash it again, but you didn't since it was already trashed, so the "If you do" condition is not fulfilled. Embargo just says $2 and place a token. That happens whether it is trashed on not, so you CAN throne room it.
I know TR-Treasure Map doesn't work, but would a TR on a Treasure Map with two other Treasure Maps in your hand work?
Treasure Map requires you trash two copies each time, then "If you do, gain 4 Golds etc... You TR it. It says to trash it, so you do, then trash a second copy, so you do. You then gain 4 Golds because you trashed the Treasure Map from play and the one in your hand. The second time you cannot trash the Treasure Map that was in play because it is already trashed. However, you MUST trash the second Treasure map that was in your hand, because the card says you must. You do not get another 4 Golds though, so really you wouldn't want to TR the initial Treasure Map.
Summary: It has to do with the "If you do" part of the card. Look at Madman. You can't TR it and I believe it even says that in the rule book.
"Nothing will prevent you from returning Madman to the Madman pile, but you may fail due to playing Madman via Procession, Throne Room, or King's Court. So, for example, if you Procession a Madman, you get +2Actions, return madman to the madman pile, draw a card per card in your hand, get another +2Actions, fail to return Madman to the Madman pile and so not draw cards a second time..."
You fail to trash Treasure Map a second time, so you may not get the second 4 Golds.
I hope that was clearer than others. Again, nothing to do with losing track of cards.