"You're doing a fantastic job," the social worker, Leo Stephens, told Compton during a telephone call last month. He said he hopes to close the case early next year.
She relies on a web of government and nonprofit services, including 25 hours of child care weekly.
Five days a week, she travels by bus to downtown Los Angeles for adult school courses required for a certificate in customer service.
"Darlene has math and writing difficulty. . . . Realistically, even though this class is only supposed to take 60 hours, it will probably take her two years," said Katherine Valenzuela, one of her teachers.
For several hours over two days, Compton struggled unsuccessfully with a calculator to total the amount a consumer would spend if he or she paid $5 every week for five years. Compton lost her temper at one point, screaming, "This is a bunch of crazy -- " using an expletive, according to accounts by both women.
On other days, she attends parenting and anger management classes, where her teacher is impressed with her progress.
"You should be teaching this class," Leroy Love told her at one point, after she provided the group with a heartfelt description of what it takes to succeed as a parent.
"A great parent is giving your child guidance and understanding your child," said Compton, whose own mother died when she was a year old. "Before, I wanted to leave my child with someone and do what I do. A great parent is making sure my child is dressed, cooking him dinner . . . being there as a parent. Not doing what I need to do."
As Compton works on her sobriety and parenting skills, Jontay spends a lot of time in the care of other people, either at a child-care center or at home, under the watch of Compton's adult son, Roy Jones.
Jones, 20, has moved back in with Compton for the first time in six years, after a bout of homelessness.
"I'm glad I can be a help," said Jones, who was raised by a variety of relatives after he left Compton's care at 14. "That's what I was born for, that's why babies are born into this world. Babies are born into this world to build, to build people's self-esteem back up, to build people's joy back up."
When Compton is home, she is often lying under a blanket on the couch, unapproachable and prone to tirades.
"It ain't ever easy," said Jones, who sometimes weathers her moods by turning up the gospel channel.
"I have this unmanageability deep down in my gut," Compton said. "I just never feel right."
But Compton ensures that Jontay is well-dressed and grooms his hair. She calls him "Daddy" and sometimes rocks him to sleep. She gave him a cellphone to play with, then marveled at how he figured out it was broken.
The boy is willful as a toddler can be, his favorite word being "no." He throws tantrums that try her patience. She wonders how to contain him, asking a friend at one point whether it's OK to "whup" a child.
"No," her friend responded, as Compton nodded, "you can always talk to a child. You can always teach a child."
Soon Compton and Jontay may be spending a lot more time together. Jones is not likely to stay long, and Compton's child-care services will end when her case is closed. Then the real challenge begins.
"It took me a long time to get to this point," she said. "God won't ever let me go back."
Times staff writer Kim Christensen contributed to this report.