This situation needs some clarity, as Sarah J says above.
When considering the generic 'child's best interests' rules, my first inclination is that anger, drinking, gambling and financial instability are not good enough to reasons to stop a child seeing his/her father, let alone cutting the father out of the child's life completely via adoption.
If I'm honest, I'm even sitting here thinking that if I were the father in this situation, I'd be going for sole parental responsibility as well - contending with a mother who thinks a father is just being uncooperative in trying to maintain some right to raise his kids and citing circumstances that pose no real danger to the kids as reasons for ousting said father from their lives completely...leaves me questioning who is more likely to be acting in the kids' best interests...