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First off great job with your twins. They are lucky to have you as their mother. In your question you mention that he has visitation every other weekend. I am sure this is court appointed and monitored by the system. My best suggestion, as it seems you have already tried conventional methods, is to contact the courts. The way he is treating the children can be seen as neglect and should be brought to the attention of the courts. I know you said you didn't want to go this direction but I think for the benefit of your children you need to at this time. If I can be of any other help please don't hesitate to ask.
I have not personally been in this situation however have helped many friends and family members deal with similar situations. Please keep my name handy as I would be more than willing to help you along the way.
YOU ARE DOING THE RIGHT THING!!