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I will try to best answer your question.
In order to completely segregate yourself from your ex it will be a long process. You unfortunately you did not get into this position overnight and you will not get out of it overnight. Although you said you were inept as your own attorney, it does seem like you've made reasonable progress towards this goal already by having him on supervised visitation with he exercises inconsistently. In situations like yours I recommend to set up as many roadblocks to visitation as possible. Supervised visitation is one such roadblock. Making him responsible to pay for supervised visitation is another. I would strongly recommend working with the children's counselors to see if they would recommend that the supervised visitation really should be therapeutic supervised visitation. This way your argument would be father could actually work on addressing abusive history between himself and the children. The idea being he would be unwilling to do this. If he is willing to do it its probably better for your children any ways than just purely a supervised visitation. The next roadblock us he needs to pay for all therapeutic supervised visitation. I would strongly advise hiring a private investigator to document his employment under the table. If you can have some documentation regarding his employment I would then recommend filing for modification of child support to increase his payments. I would further recommend that when you are pushing the issue of increased child support you can suggest the idea that he discontinue visitation in exchange for you only accepting the derivative benefit for the children from Social Security as support.
Finally, if at all possible try to relocate farther away from father. You will not be able to tell the court that this is your motivation, but instead tell the court that is necessary for employmentfor other reasons that have nothing to do with custody.
I hope that this information and suggestions are helpful and I wish you the best of luck with this difficult situation.