Prosecutors objected to the request.
A federal grand jury in September indicted Mitchell, sons Dryden Mitchell and Nick Mitchell, six other men and a Costa Rican company.
Teddy Mitchell is accused in the indictment of making millions of dollars by hosting illegal high-stakes poker games at his home and by illegally taking bets on sporting events. His attorney contends he is a professional gambler who acted legally.
The judge Tuesday did give Teddy Mitchell permission to attend recreational golf outings with Dryden Mitchell and Nick Mitchell. The judge also allowed them to attend Alcoholics Anonymous meetings together.