A national visa (D-visa) is only issued in exceptional cases. According to the law, special circumstances must apply in your case. A family visit is not considered special circumstances, or that the processing time for a visitor's permit might be longer. The fact that you have previously been granted a D-visa does not automatically mean that you can get a new one.
Applications for national visas are submitted at and decided on by the Embassy. If you have special reasons for wanting to stay in Sweden for longer than 90 days, kindly email the Embassy on ambassaden.lusaka-migration@gov.se with your personal information and we will guide you to what permit or visa to apply for.
In order to apply you need:
The Embassy reserves the right to ask for further documentation if needed.
The decision is made at the Embassy. You cannot appeal against the decision if it is refused.