It was not the responsibility of the mother to close the case in Hawaii after she moved to Oklahoma. What happens is she registers the order from Hawaii in the state of Oklahoma.
Pursuant to the U.S. Constitution, Oklahoma is then obligated to enforce the order from Hawaii as it exists under the laws of Hawaii.
After the mother and child (and you) are no longer residents of Hawaii (usually for 6 months), the Family court in Oklahoma will then usually assume full jurisdiction over the case. When they do this they are supposed to let the court know if Hawaii that they have assumed jurisdiction (due to a lack of any party residing in Hawaii anymore) and Hawaii is to close their files.
Now Oklahoma has sole jurisdiction. This means that if either party wanted to file a motion for a modification of custody or support they would file their motion in the county courthouse in Oklahoma.
At this point I suggest filling a motion with the Family Court in the county in Oklahoma where the order was registered and is now entered. You need to specifically request that the judge issue an order to Hawaii informing them that his county family court has assumed full jurisdiction of the case and will be handling all requests for modification and enforcement.
As long as you have the proof that Hawaii is still insisting on collecting the child support (and you have wisely been keeping these statements) the judge should have no problem issuing this order. The Clerk of the Court will then usually take care of filing the judge's order with the court in Hawaii.
You should be able to do all of this by mail without having to go to Oklahoma. You can usually call the Clerk's office and ask them to fax, e-mail or mail you any official forms needed to file a motion. They may also be able to tell you if they are available on the web, but sometimes the forms on the websites are not the latest forms.
You do not want to waste you time completing a form you took from the internet that was just replaced last month as the court will likely reject it.
Please let me know if you have any questions about this.