Under Cal. Family Code 7822(a)(3), a parent may bring an action to terminate the parental rights
of the other parent if "One parent has left the child in the care and custody of the other parent for a period of one year without any provision for the child's support, or without communication from the parent, with the intent on the part of the parent to abandon the child."
Given that the original paternity judgment was made in California, the Arkansas court would have to consider California law in determining whether or not it has authority to terminate the father's parental rights. Based on your allegations, it seems that it would not be difficult to prove that there has no been no support or communication from the parent for the requisite 12 month period. But, that's what you would have to prove.
Assuming that you could do this, then you could prevent the father from exercising any custody, or other rights concerning the child. Otherwise, unless that parent consents to a step-parent adoption by your husband, then the Arkansas court would be obligated to permit supervised visitation
, with the possibility of increased visitation over time.
I realize that the possibility of forced visitation with the bio-dad is probably nauseating -- and it may be for the child, too. If so, then you would be entitled to ask the court to terminate all visitation, until some sort of reconciliation plan could be worked out.
More than likely the bio-dad is trying to leverage his parental rights to get you to agree to compromise his arrears, so he can be free of the obligation of child support forever. You may want to use this negotiation leverage to get his consent to the stepparent adoption
. However, you must be extremely
careful about how this is handled -- because a payment or forbearance of a debt in exchange for custody/parental rights, is quite literally the definition of slavery (which is a felony). Parents cannot buy or sell parental rights.
That said, this sort of under the table arrangement does in fact take place with some routine, despite its illegal underpinnings. You just have to handle it through a lawyer and maintain nothing in writing.
So, if that's what it comes down to, and it seems as though it very well may, then get a lawyer with adoption experience, and try to negotiate something with the bio dad to get him to go away quietly.
Hope this helps.