I'm married and have a son who's dad lives in Missouri and wants to give up his rights to his son and my husband wants to adopt him but how do I go about this do I go through Missouri or do I go through Tennessee court?

How long have you lived in TN? Generally, you file where the son has residence. But since you really need an attorney to prepare the adoption petition,just shop around for an attorney. The attorney will prepare the petition including getting the bio dad's agreement.

BTW, its not about the dad wanting to give up rights. Its about your husband wanting to adopt. Unless he agrees to adopt the bio dad will not be allowed to relinquish rights.

This will go thought the court where the adoption will take place, if the bio father does not object you file where you and the child live, you hire an attorney, he writes up the adoption, sends the forms to sign over his rights to the bio father, the rights will end on the day the adoption becomes final.