I think you know the answers to your questions are obvious. Here are some more questions with obvious answers:
Should you continue in a relationship where your partner has a continuing dependency on drugs and alcohol?
If that's your kid in the picure, is this the kind of example you want to give your child? Not just his example of using but also your example of accepting that behavior in your family.
Do you believe this man loves you enough to stop? If so, why hasn't he? If he claims he has, and you believe he does love you enough to stop, then what is making you distrust him? Could it be your instinct trying to steer you away from a negative relationship- but you don't want to listen? It's never to late to make a good choice for your family.