"We have a great respect for Jay Leno but we are disappointed in the path he chose to allow a guest to make light of a very serious situation concerning Lindsay," Dina told Access Hollywood's Billy Bush in an e-mail Thursday.
On Tuesday, Schneider was booked as a last-minute replacement for Lohan, who canceled her scheduled appearance after she was arrested on drunk-driving charges. For the spot, Schneider dressed in drag as the actress, complete with blond wig, black dress and an alcohol-monitoring bracelet strapped to his leg.
"This is a very personal and private matter and our only concern is to get Lindsay the help that she needs," Dina adds in the e-mail. "We will get through this together and it will make our family stronger."
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She added: "Our thoughts and prayers go out to all families who have had to see a family member through tough times."
The email is signed, "Dina and Family."
Paul Drinkwater / NBC