I'd say it means they are determined to share driving duties.
Yes, that makes sense to me. I think it may also simply indicate that they are ready to share driving duties.
For instance, "They are set to begin their journey" simply means that they have done what they need to get going.
If you add "look" it simply means they "appear to be." Hence, "They look set to begin their journey" means it appears to you that they are ready to go. They may be eager to do it or may be gritting their teeth in anticipation of a hard journey; it is hard to say.