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The troubled actor had his plea rejected by judge Hank Goldberg at the Stanley Mosk Courthouse in Los Angeles on April 19.
Sheen had hoped to win primary legal and physical custody of two-year-old twins Bob and Max after Mueller refused to take a drug test on April 15 and entered rehab.
According to RadarOnline.com Mueller - who attended court - seemed "unsteady on her feet" and "glassy-eyed" at the hearing, but smiled as she left, while former Two and a Half Men star Charlie - who is currently on his Violent Torpedo of Truth/ Defeat is Not an Option tour - only added: "No comment."
Every other weekend
The decision maintains the situation decided in court on March 10, which sees Mueller have majority custody of Bob and Max while Sheen will be allowed to spend time with them every other weekend from Saturday morning until Sunday evening for the first two months.
For the following two months, he will have the children every other weekend from Saturday morning to Monday morning. After that - provided both he and Mueller stay alcohol and drug free - he will have them an additional Wednesday morning through to Thursday morning.
Mueller's mother, socialite Moira Fiore, is thought to be providing primary care for the boys while the 33-year-old is in an unnamed rehabilitation facility after reportedly relapsing into crack cocaine addiction last week.
