While it is true that in most cases a DUI conviction renders a person inadmissible for entry due to criminality, there is a process for getting a 'second chance' at entry.
Canada can, under certain circumstances, issue something called a "Temporary Resident Permit". It is meant to allow a 'rehabilitated' person with a record to enter the country where there is little chance of that person behaving badly in Canada.
I would think that travelling through Canada with his parents and son would present exactly that kind of extremely low risk.
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