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"Lindsay has been given a new start and will put this behind her," Dina told PEOPLE Friday.
Lindsay Lohan spent 84 minutes in the jail as part of her plea deal in her two DUI cases.
"She is focused on educating others of the dangers of drinking and driving," the elder Lohan said of her daughter, who began her community service on Tuesday.
The actress – who recently completed rehab at the Cirque Lodge in Utah – was also placed on three years probation and must complete an 18-month alcohol education program.
Of Lohan's 84 minutes behind bars, her father Michael Lohan, who was released in March from a state prison near Buffalo, N.Y. after serving almost two years for charges including D.U.I., tells PEOPLE: "I'm happy she got through it."
JOSH & FERGIE: ROCKED BY SCANDAL
Did he cheat with a stripper?
Married less than a year, the couple denies an Atlanta woman’s claims that she and Josh had a fling
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