"She's going on with everything," the source tells PEOPLE. "She's sad, but she's okay."
In fact, Simpson, 32, who is now a spokeswoman for Weight Watchers, has been going along with her routine, which lately has included returning as a mentor on the NBC show Fashion Star, planning a Halloween party for her 5-month-old daughter Maxwell and friends, and making regular trips to the gym to work out with her trainer, Harley Pasternak.
Four days per week, "no matter how tired is, she goes to the gym," the source says. "She keeps her workouts the same."
Meanwhile, two days after a rep for the family confirmed his split from Tina Simpson, Joe Simpson stepped out without his wedding band.
"It is an amicable split and there is no third party involved," the rep said. "Any other related allegations are completely false. The family appreciates your respect for their privacy at this time."