The mass driver makes an excellent, continuous-fire cannon.
It expels big rocks at 30 m/s. The minimum escape velocity of 243 Ida, at its "pointy" end, is roughly 11 m/s (wiki the asteroid and work it out). So, after the expelled rocks have left Ida they should be moving at about 19 m/s. Dactyl orbits near (8 degrees away from) the equator, so it passes over the pointy end of Ida. Dactyl is tidally locked which means that the cave is always facing Ida.
So the brothers pick up the drill and mass-driver and tow them to the pointy end of Ida (we can see that they can push them around in the tiny gravity). They fire a burst of rocks into the cave on Dactyl. They adjust their aim simply by watching the stream of rocks and adjusting the aim of the mass driver. At 19 m/s (roughly as fast as a fast thrown baseball) a rock the size of a man's head would punch a hole in a shuttle. A stream of such rocks will demolish it. Fire just enough of a short burst to scare the crooks to come out and try to flee, then pour it on and destroy them.
Whether the brothers inadvertently disable their own shuttle is a matter of a bit of luck. But after wiping out the bad guys they could then get to Dactyl like this: step down the ejection speed of the mass driver so that it is ejecting at orbital velocity, then one man gets in it ("human cannonball") and is fired into the same orbit at Dactyl.
Piece of cake.

I can hardly wait to be an anarcho asteroid belter.