Charlie Sheen Says Sons Appreciate He's 'Not Dumping on Mom' Brooke Mueller amid Alleged Relapse (Exclusive)

• Charlie Sheen and Brooke Mueller continue to share custody of the 14-year-old twins, but it is contingent on her sobriety
• Sheen recently celebrated his sixth anniversary of sobriety and is focused on raising his two youngest kids
• Mueller has allegedly been struggling with maintaining her sobriety, which the kids are grateful Sheen is sensitive to

Charlie Sheen has earned the pride of some of the people closest to him.

Speaking with PEOPLE last month, the Two and a Half Men actor, 58, talked about his relationship with twin sons Max and Bob, 14. The father of five — who also shares daughters Sami, 19, and Lola, 18, with ex-wife Denise Richards, and 39-year-old Cassandra Jade Estevez, with ex-girlfriend Paula Speert — said that his youngest pair appreciates both his sobriety and how he handles mom Brooke Mueller's alleged struggles with her sobriety.

"She's trying to figure some stuff out on her end," he acknowledged.

"The boys are proud of me, now. They see what mom goes through, and I'm not dumping on mom because I know it's a thing," he added.

"But I think they're super grateful that they have a Dad that is present, accounted for, responsible, focused, punctual."

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In recently filed paperwork that adds stipulations to the custody agreement between Sheen and Mueller, an agreement between the two states that they will "continue to enjoy joint legal custody" unless Mueller tests positive for drugs and alcohol or otherwise relapses. At that point, Sheen would have sole custody "until further court order or written agreement of the Parties," and this could happen on as little as 48 hours' notice.

The two also share physical custody of the boys, though the paperwork sets for that "the minor children's primary residence will be with [Sheen]."

"Brooke shall enjoy reasonable and flexible periods of custody and visitation as agreed and arranged between the Parties, recognizing the goal of frequent and continuous contact between the minors and both parents."

The agreement also says Mueller will undergo drug and alcohol testing weekly at minimum, as well as "as often as required by her probation officer" or "within 24 hours of a written request (email or text) from [Sheen] or his attorney," which they have the right to continue until the twins turn 18 or graduate high school (whichever is later).

The documents also state that the actor, who recently celebrated six years of sobriety after his own struggles with drugs and alcohol, is currently paying Mueller's rent and will continue to on condition of her sobriety, though he will not serve as a co-signer on any new real estate moving forward.

In the event of relapse, Sheen reserves the right to terminate all financial support of Mueller, leaving her responsible for any costs of securing a new residence.