Dina Lohan tells PEOPLE her daughter is "getting a grip on her life" by entering rehab

A day after Lindsay Lohan revealed that she’d checked into rehab, her mother tells PEOPLE that the actress is “absolutely fine.”

“This is a wonderful, giant step she’s taking and it’s all good,” Dina Lohan said Thursday. “Hollywood’s a really, really busy scary place and everything is under control.”

Dina says she’s proud that her 20-year-old daughter is mature enough to take care of herself and “not worry about what anyone’s going to say about her.”

On Wednesday, Lindsay said in a statement that she had made the decision to enter rehab in order “to take care of my personal health.”

As for how Lindsay is doing: “Everything’s great and she’s just getting a grip on her life,” says Dina. “When I was 20 I don’t know that I would be that strong to do that, so it’s all good.”

The facility where Lindsay is being treated, her mother says, “It’s an outpatient program where, of course, (she’ll be) in for the first week or two.”

After that Lindsay plans to get back to work on her film, I Know Who Killed Me, which has temporarily suspended filming.

“Then she’ll pick up the film again and start working and have someone with her and all is good,” says Dina. “As a parent I couldn’t be more pleased and proud.”

Meanwhile, a source close to Lindsay says the actress made the decision to seek help on her own: “No one told her to check into rehab. She’s doing it to get herself together, to focus on the movie that she’s doing right now.”

The friend adds that before, it was hard for Lindsay to fit her AA meetings around her work schedule. “This program meshed far better for the schedule of filming and dealing with her demons.”