I'm getting the same glitch with Time Traveller, Scientist, and Knight.
The first time I thought it was a fluke, but I replayed and got the same result: After the Mine Cars stage, the only way to proceed takes me to the Twins Mansion. My characters can do a few things, but without the Twins' power I can't enter the mansion. In addition there are Twins cave paintings which none of my characters can touch--which is strange, because normally any character can grab any cave painting.
@nulian, I did find my way into the sewers but these three can only get that far without Twin powers.