The problem of the outer wheel going farther during a turn also occurs with trains, and trains do not have differentials to let the wheels have different angular velocity. On a train, the inner and outer wheels have the same angular velocity regardless of turns.
I'm linking to Jalopnik, which embeds Richard Feynman's video on train turning, rather than directly to the video because there are some interesting comments on the site. In particular, see the comment from railroad employee "Gonemad" about how they have a system that automatically greases the wheels before turns, which seems rather counterintuitive at first.
How trains accomplish this is interesting: http://jalopnik.com/5820296/how-trains-make-turns-without-di...
I'm linking to Jalopnik, which embeds Richard Feynman's video on train turning, rather than directly to the video because there are some interesting comments on the site. In particular, see the comment from railroad employee "Gonemad" about how they have a system that automatically greases the wheels before turns, which seems rather counterintuitive at first.