07/01/2007 at 11:20 PM EDT
Three days after Britney Spears
handed her mother a reportedly upsetting letter, Lynne Spears is holding out hope to mend their rift.
"Everything is going to be fine," she told PEOPLE while shopping in Kentwood, La. "I've got a strong family, and everything is going to be fine."
Spears, who was picking up groceries at a local store on Sunday, also said that "hopefully" daughter Britney will make it to a family cookout in their hometown for the Fourth of July holiday.
Meanwhile, Britney Spears was spending her weekend in L.A., going out Friday night with girlfriends to club Les Deux but appearing subdued as she chatted and bounced to music.
On Sunday she spoke to reporters about her mother outside Sushi House Unico in Bel Air, where she had dined alone on edamame and coffee.
"I'm praying for her right now. [I hope] she gets all the help she needs," Spears said.
Whether the two can overcome their differences, she said, "In time, who knows what will happen?" Spears also insinuated that she likely would not go to Kentwood for the holiday, saying, "I don't know. I like it here."
A few days earlier, on Thursday, Spears was snapped by paparazzi handing her mother a piece of paper that TMZ.com
reported to be a request from an out-of-state lawyer.
According to TMZ, the letter asked that Lynne stay away from Spears's sons Sean Preston, 1, and Jayden James, 9 months, if she is taking any medications that might cause her to be impaired.
As for what may be behind the rift that has left Lynne Spears apparently "brokenhearted," a family friend told PEOPLE on Friday
: "I think Britney is angry that her family got involved in getting her into rehab."
In February, Spears checked into Promises Treatment Center in Malibu.
Reporting by RUTH LANEY and BRENDA RODRIGUEZ