After revealing her decades-long battle with alcohol addiction in November, this week Vargas, 51, announced she has returned to rehab, checking into a facility while on vacation.
It's an ongoing struggle she admits has taken a toll on her family, including her husband, singer-songwriter Marc Cohn, and their sons Zachary, 11, and Samuel, 8.
Now, a source with knowledge of the situation tells PEOPLE that Vargas has another trial to face: divorce.
"Marc and Elizabeth are in divorce proceedings," the source says. "The kids are with him in New York while she seeks treatment."
The couple wed in 2002. Despite the split, the musician, who's currently on break from touring, issued an exclusive statement to PEOPLE, offering support for his estranged wife.
"On behalf of Elizabeth's family," Cohn, 55, writes, "we are in total support of her recovery and want her to be well."
In her own statement this week, Vargas said, "I feel I have let myself, my co-workers and most importantly my family down, and for that I am ashamed and sorry."