Family reunification with a PhD Student

My wife is a PhD student at the University of Antwerp. On September 30th we came to Antwerp from Turkey and since then we have been living in a rented house. When we came here, my wife came with a temporary student visa for 4 months and applied for a residence permit. The process is ongoing and yesterday she received her "Temporary residence document Bijlage 15".

My son and I came with a "Service Passport" from Turkey. Since my wife and I work as academicians at a university in Turkey and my wife was assigned to stay here as a student for 1 year, we can travel without a visa with a service passport. But our right to stay in the country with this passport is not to exceed 90 days in 180 days. So we can stay here until December 30 at most.

Also during this period, with the advice we received from "Atlas", we enrolled our 11-year-old son in a school here for his education.

After my wife gets her residence permit here, we need to apply for a "family reunification" visa in our country. It can take a long time to arrange an appointment and wait for the application. Normally, since Turkish citizens cannot travel to Europe without a visa, they cannot travel with the person who will request family reunification. Since we have a service passport, we came together to ensure family unity.

After she gets her residence permit, can we apply for family reunification without going to Turkey, does anyone have information about this issue, I would appreciate if you can help me. If we go to Turkey after December 30th, we have to wait until the visa is issued. With a service passport we can come at the beginning of April at the earliest. I wonder if we can apply here for the continuation of our son's education and for the protection of family unity.