I am not licensed to practice in your state, but here in Florida there would be no reason to pursue child support through the juvenile court in this case. Juvenile court will only become involved in situations where children are alleged to be abused, abandoned, neglected or ungovernable. The court having jurisdiction over your divorce case would have the authority to order child support, and, in fact, will probably be required to do so. Many states, like Florida, have statutory child support guidelines and a judge, in ordering child support as part of the divorce decree, cannot deviate from the guidelines without making specific findings as to why it's being done. If this is the case in Tennessee, even if you and your husband agreed on a lower amount of child support than the guidelines suggest, your judge might not allow that. It sounds as though your divorce will have to proceed to trial on a contested basis because the two of you do not agree on this issue.
My suggestion to you is that you need to consult a divorce lawyer to help you determine what is appropriate and in the best interest of your children. Your local bar association may have a legal aid office or a lawyer referral service offering low-cost legal assistance. Another alternative may be for you and your husband to seek the services of a mediator to help you sort this out. I'd advise you to call the court clerk's office to see whether mediation is available at the courthouse.
I wish you all the best.