The trouble that the DM in the original post is having is a problem with adventure design, not with whimsical players.
You have to become more familiar with the "No Myth" DMing style. As a DM, you should always avoid giving out specific and concrete information about the setting until you absolutely have to. This allows you to change the setting on the fly in response to player actions without tipping off the players about your actions. It takes a lot of its flavor from quantum physics, in that the state of the setting isn't fixed until the PCs actually need to know about it.
For example, you've set up an adventure in the traditional mold. I refer to this as "making a pre-published scenario when you don't have to." All DMs have bought published scenarios and mistakenly assume that the format of a published scenario is how they should format their own scenarios. This is utterly wrong. The format of published scenarios is meant to be helpful to a broad range of different groups of players. Published scenarios are sterile.
So DMs unconsciously adopt the published scenario format. There will be a story in place, NPCs will be planned in advance and statted out, there are locations with particular descriptions that contain particular items, etc.. This format is too rigid. It's too tightly woven together. In a way, it has a kind of threshold. It all works together provided that the PCs reach a certain point in the scenario where they become committed to the entire package. I guess that's an elaborate way of saying that they are all predicated on the PCs taking the hook.
Your problem isn't that the PCs aren't taking the hook, but rather that you're falling into the published scenario trap of building the entire dungeon/scenario around that hook. If the PCs aren't hooked, the rest of the scenario is built on that hook and is useless. You need to stop doing this.
My first instinct when trying to answer this question was to suggest that you move the dungeon. Arrange it so that the players travel a hundred miles but end up in the same dungeon anyway. The difference would be that you would have to change the details of the dungeon sufficiently so that the players won't notice. This is crucial.
The players have never been to the dungeon, so they don't know what is in it or what it looks like. As long as you change the information that the PCs do know, they'll never know that they ended up in the dungeon you wanted them to end up in!. Maybe an example is in order.
In the scenario described in the initial post, the PCs are on a tangent of some kind. This occurs for one of two reasons (that I can immediately think of): (1) the PCs think they are on the right track for a particular storyline but are in fact going off on an inadvertent wild goose chase and (2) the PCs are just going "where adventure takes them" and are following an obscure rumor of adventure (or something similar).
In the first situation, the DM must simply move the dungeon. If the PCs think that the clues leading to the Lich-King's lair point to Waterdeep (to use Realms geography) when the DM has intended the lair to be in Shadowdale, then just move the lair to Waterdeep! Here's the trick. The DM has laid out clues that he believes will build a chain that leads to the conclusion that the lair is in Shadowdale. The players, however, have used the same chain of clues to (perhaps mistakenly) deduce that the lair is in Waterdeep. From the DM's point of view, the players are "off-track".
But from the players' point of view, they're right on track. The DM has two choices. First, he can break the flow of his campaign by forcing the players to return to Shadowdale. The DM has invested a lot of energy in designing the lair and doesn't want to have to improvise a dungeon, which is hideously difficult. But the players are likely going to recognize that the DM is railroading them back to Shadowdale.
The better option is for the DM to abandon his version of the "clue chain" and instantly decide that he's going to go with the players' version of the clue chain that leads to Waterdeep. So he moves the dungeon from Shadowdale to Waterdeep and into the path of the players. The DM has saved his carefully prepared dungeon and the players maintain the illusion of free will. From the DM's point of view, the players were going to go to the Lich-King's lair one way or the other. This second alternative, however, preserves the all-important illusion that the players are driving the game. The game reamins seamless from the players' point of view, which is what matters.
If the PCs are following the second option ("wander the world and stumble across adventure"), then the DM should have a selection of "stock" dungeons ready to go. They should be flavor-free but contain all the mechanics, layout, and monsters that he needs. When the players make it clear that they're looking to stumble across a dungeon, the DM just drops the stock dungeon into place and merely has to improvise the superficial details of the dungeon, like what it looks like and where exactly it's located.
