"Jen is doing well," a source close to the family tells PEOPLE. "She's still adjusting to a new normal, but seems more accepting of the separation."
While the source notes that Garner is "taking a little bit more time to herself" and "seems less stressed," moving forward with her love life is not a top priority at the moment.
"She can't even imagine dating," the source says, adding that "it will probably be a long time before she is able to move on romantically."
In the meantime, Garner and Affleck continue to put their children first, and spent time together as a family over the weekend.
After taking a few days to scout locations in Savannah and Boston for his new movie Live by Night, where another source close to the couple says he "had a really great time seeing his family," Affleck returned to L.A. on Friday to drive his daughters, Violet, 9, and Seraphina, 6, to school.
VIDEO: Ben Affleck and Jennifer Garner All Smiles as They Step Out Together in L.A.
Later in the afternoon, he drove them to karate class, where Garner joined him to watch the kids at practice.
On Sunday, they had a family outing at a local farmers' market and also attended a church service.
"Ben and Jen mostly spent time separately at the farmers' market," an eyewitness tells PEOPLE. "Jen picked up fruit and vegetables with a nanny while Ben was in charge of the kids. He took them to get balloon art and entertained them while Jen shopped."
According to the family source, "Ben has a schedule when he is responsible for the kids." He "is still living elsewhere" and he and Garner have "no plans to live on the same property."
The family home is currently undergoing renovations, and the source close to the couple tells PEOPLE that they "redid the house so that they could cohabitate."
"They may not live [there] together," the source adds, but the house remains a place "where they can help raise their children together."
The divorce, meanwhile, is moving forward as planned, the family source tells PEOPLE, adding that neither Garner nor Affleck "seem rushed" when it comes to hashing out the details.
"Ben wants her to be happy," the source close to the couple tells PEOPLE. "Ben truly cares for Jen and really wants her to be happy overall in general."