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It would be highly unlikely. I say this because when determining custody issues, a court is going to always do what it feels is in the "best interest of the child
(ren)." So they're going to look at a number of factors - who the main caregiver of the children is, who is in a better position to best support the children, the emotional, physical and mental health and welfare of the children, if the children are older (usually beginning around 10-12) the wishes of the children, etc.
Here, the father of the children has a lot of negatives against him. He abandoned the household. He has had no/limited contact with the children even though it's obvious he knows where you are and how to reach you. And, he hasn't supported them, despite the fact they also have disabilities, making that support, I am sure, even more important. You also mention domestic violence. If he has been violent towards you and/or the children, that is another factor the court will pay close attention to and consider. In other words, when looking at who the children are better off with...based on these facts -- it is you, not the father.
That is not to say a court wouldn't give him some sort of visitation with his children. A court wants children to have a relationship with both parents whenever possible and not cut a parent out of their life, so long as a parent is not a danger to or harming that child. If he has harmed the children in the past, then the court may give him no visitation rights, or extremely limited visitation or even perhaps limited supervised visitation
only with the children.
Please let me know if you need any clarification or additional information.