ADDED after your SWH and some other responses:
I think a big question here is: Is this professional theatre, which would be subject to state laws and union rules, or is it amateur theatre/kids' theatre which might not be under the same restrictions? If these are shows with lots of kids and the parents do drop them and leave, then for now at least, the issue of state working laws and union laws don't apply, I guess -- but your sister should check, and should be aware that if he moves on into any professional productions/union shows, a parent may indeed have to be around. Something for her to have in her mind if he keeps acting. From what you say, it sounds as if a hired person would help, but if they are striking out with colleges, what have they tried? Did they look at colleges' online job boards (some colleges run these for students), did they advertise in the college newspaper, put up posters on campus bulletin boards, contact the "student life" office? They may have to put out some different kinds of effort to reach college kids. But one thing to remember about them too -- their schedules change each semester or quarter and they may have a tough time finding one student who can do it consistently all year long....it sounds as if your nephew does not have an agent or anything that formal. But if he does, or gets one, the agent could be of help arranging transportation.
I understand the issue -- my daughter dances and many weeks has classes and/or rehearsals four of the weekdays and at least one weekend day, and I know theatre can be even more grueling, with more performance dates involved.
I was going to second the idea of a reliable college-age person until I read the statement that "he has Asperger's and getting him to do anything but act is very trying." It's the latter half of that which really concerns me -- if the Asperger's means he gets fixed on doing something and can't be flexible, then he really does need someone with him, actually at rehearsals and performances, who knows him and how he reacts to things, and -- very importantly -- whom HE knows well enough to listen to. If your sister and her husband hire a car service, there's no adult in the theatre for him; if they use a nanny or college kid, however great they are, those are still relatively strangers to him. Will they be able to calm him if he gets worked up, upset or angry over something a director says to him? Will they be able to tell a director or producer to hold off a minute while they deal with him or will they be afraid to speak up like that to his "boss" on the boss's turf, the theatre?
A lot depends on things we don't know here, such as whether he tends to get angry or upset over things easily, or if his Asperger's is a mild condition where it's not so much of an issue and he's fine left alone for several hours in a rehearsal.
But as another person noted -- if he goes on with acting he needs some adult protection. I think that's true regardless of the Asperger's. One production may be fine and full of family-like atmosphere and good treatment of kids, and it feels just fine to leave him there for hours. But another another production may have a bully of a director or a short-tempered producer or other kids who think they're stars, or be in a theatre in an area that's not as safe. He really needs someone he knows there. I do leave my daughter -- who is his same age, 11 -- alone at rehearsals, but she is with the same adults she sees and takes classes from every single week, several times a week. He would be with changing sets of adults he doesn't know except during that one production.
So I'd advise them to shift schedules, tag team things, sometimes see about trading off "stay for the rehearsal/drive both kids home" with other young actors' parents, IF there are other kids in the show, though that might work out only rarely.
In other words -- I hope they do all they can to make theatre work for him if it's his passion, but Asperger's or no Asperger's, I'd have a parent there for him for at least a while to come.
Eleven is old enough to have found a love of theatre, but not yet old enough to navigate dealing with adults whom he doesn't know very well, and who do not know him very well.