"Brooke wakes up in the morning and works out," says her mother, Moire Fiore, who has been spending time with her daughter in Palm Beach, Fla., this week. "[She is] feeling positive about staying in the best physical shape for her twin sons Max and Bob."
Mueller and her boys are also enjoying being together, according to Fiore. "She dressed them up as crayons and took them trick or treating in Los Angeles on Halloween," Fiore tells PEOPLE. "They looked adorable."
Sheen, 45, and Mueller, 33, each filed separate divorce petitions in Los Angeles Superior Court on Monday. In a settlement agreement hammered out in May, the ex-couple's 19-month-old twins will live primarily with Mueller with generous visitation for Sheen.
Both cited irreconcilable differences as the reason for the split, and both agree that they separated on Christmas Day following a fight in Aspen. The case ended with the actor pleading guilty to misdemeanor assault.
Last week in New York, Sheen was hospitalized after he was found intoxicated in a hotel room. His rep says the actor had an allergic reaction to medication.
For her part, Mueller is preparing to begin shooting a reality show for the Oxygen Network later this month in Los Angeles with Paris Hilton.
"Brooke looks forward to the new TV show and knows how important it is to stay strong for the boys," her mother tells PEOPLE. "She is doing phenomenally well."