You're using anecdotes in lieu of actual data. Your cousins are not evidence.
Moreover, were illegitimacy the causal factor, Hispanic and Black rates of crime would only be double and triple the White rates. This is not the case: colorofcrime.com
It is true that illegitimacy is a rough start to life, but there are other causal factors of crime such as low intelligence and impulsivity. Both Blacks and Hispanics have lower average intelligence and, if you've ever worked around Blacks, you'd know how impetuous they can be.
Illegitimacy and poverty are just the conservative and liberal fairy tales to explain away the horrendous failures of minority groups.