To go from a varchar date: 'dd/mm/yy' to a mm/dd/yy datetime in SSIS, you could use something like the following as the expression in a derived column transformation:

ISNULL(CHAR_DATE) ? NULL(DT_DATE) : (dt_date)(SUBSTRING(CHAR_DATE,4,2) + "/" + SUBSTRING(CHAR_DATE,1,2) + "/" + SUBSTRING(CHAR_DATE,7,2))

If you didn't have the freedom to modify the data type from varchar to datetime, you could still do something similar, but I absolutely agree with Jeff, try to avoid storing dates as varchars if you have the option.