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1.
Taken from the John Ritter movie by same name. Used to describe any child, employee, sibling, or friend that is constantly getting into trouble but you are somewhat obligated to care for or help.

Also a street name for someone who gets into trouble all the time.
Frank, the departments problem child, forgot to lock the office last night.
by Blowfish July 24, 2005
 
2.
A "strong smooth drink" that will fuck you up! : consists of Tequila, Vodka, Lemon Juice, Lime Juice, and Tonic Water
Ashley: "Hey Mike, Netflix went out because of the weather"

Mike: "Make yourself a problem child and and you'll be straight!"
by flipflop1 April 23, 2011
 
3.
vodka soda
yo, barmaid, I'll have a problem child please.
by pepsi123 December 18, 2010