Largely within the real of the Point 'n' Click, which is altogether a friendly genre to this sort of game.

Sierra is probably the company that has created the closes analogue to your idea, with their relatively obscure edutainment title Pepper's Adventure in Time (currently Abandonware, hunt it down for use with ScummVM if you like). Which does feature a kid in a time machine who has to fix horrible problems created by a Big Bad (her evil uncle Fred) while learning about history.

Sierra did a similar, albeit less educational, idea far, far earlier, with the game Timezone, but that game stands out as a uniquely horrifying mess of a game even by Sierra's much-maligned standards of playability, solubility, and... well, sanity.

There are other games that have done this idea, I swear, but the closest that comes to mind right now is Day of the Tentacle, which has three kids (one in the past, one in the present, one in the future) all trying to fix a time machine to get back to the present and stop and evil tentacle from taking over the world by preventing him from drinking the toxic sludge that turned him evil. No, it's not quite what you had in mind, but it is very funny, and it's one of Lucasarts' best, which means it's de-facto in the running for Very Greatest Adventure Game Ever Made Ever. So at the very least I can suggest that you play it if you're into that sort of thing.

It doesn't sound like a natural fit for a Massively Multiplayer Online Role-Playing Game (how would the plot accommodate more than one protagonist?), but it does sound interesting.

It reminds me a bit of Quantum Conundrum, notable for cross-dimensional puzzle shenanigans and extremely entertaining voice acting by John de Lancie. Oh, and it was directed by one of the people behind Portal, which makes total sense in retrospect. (Phobos played the game, I just watched.)

~Neshomeh