Can it be ordered that father not get custody...?

In the event that I die (hopefully that won’t happen!), is there any way to have it ordered that my ex NOT get custody of our son? He is an admitted drug addict, who has refused to seek help to get clean. He currently is not even allowed (per court order) to see our son at all. Is there anything that can be put into the divorce/custody that would prevent custody of our child going to him in the event of an untimely death for me? Is that something that my lawyer could request, given the circumstances? (we are having to go to court on all issues because stbx will not agree to ANYTHING)

Also, is there any way to terminate his parental rights based on the fact that he refuses to help support his son and is an addict who refuses to seek help? He does call him about 3x/week, but my son never wants to talk to him, and the calls last approximately 1 minute each, and generally consist of my son telling him “I don’t want to talk to you”.

No, as a natural parent whose rights have not been terminated he would automatically get custody of a child unless rights have been terminated. I have seen a custody order in which the parties attempted to dictate who would take custody of the children in the event of a parent’s death and the judge refused to sign the order, even though the parent’s both consented to the stipulation in the Order. In the event of your death, social services can intervene in the even the child is not in a suitable home.