I don’t believe courts actually order people into AA. A person is found guilty and is offered the choice between voluntary participation in a treatment program or incarceration. Any qualified treatment program would do. AA is free. The others charge. AA probably becomes a default option for that reason, but I presume someone could ante up the bucks for a fee based program if he had some objection to AA.
Depends on the jurisdiction, and if this battle has been fought before. Back in the day when the only treatment programs the average person knew about were AA and Betty Ford it was often specifically listed as AA. Slowly but surely that’s been unwinding and getting more open, but they do still tend to lean towards “12 step based” programs, as that has a lot of brain real estate.