I just assumed Rozemyne was going to teleport from Kirnberger directly to Dunkelfelger then directly to Ahrensbach there by bypassing the Sovereignty completely and not needing to get permission or the royal family's involvement. And though I imagine it would be convenient for the Zent to have a teleporter connecting each country gate to the Sovereignty, I see no mention of that in the books at all.
The Zent had the power to create teleportation circles between duchies—and, since the country gates existed outside of the aubs’ borders, he probably hadn’t even needed their permission to make them. - P5V4 (Kirnberger's County Gate)
Creating an interduchy teleporter to Dunkelfelger's border with Ahrensbach would have been a fast travel option, but there are some reasons it may have been unfeasible.
To prevent assassinations and ambushes, only the archduke could place the kinds of teleportation circles used to transport people—and these circles were limited to travel within the duchy. Those used to cross duchy borders, such as the ones that provided access to the Royal Academy, required the king’s approval. - P4V9 (Finding the Book)
Human teleportation was so consequential that only aubs could make and operate the means to it. - P5V4 (Archducal Family Meeting)
“What a waste...” I muttered on instinct. Making teleportation circles required a variety of materials. - Matthias P4V9 (Out of Time)
Just the time to make the teleportation circles may have prevented it from being an option considering all the things both archdukes need to do to prepare. Rozemyne intended to ask Aub Dunkelfelger to place teleporters between the country gate and the gate bordering Ahrensbach until Justus informed her that Ahrensbach's border gate near the country gate was open. This probably would have been a problem considering the above mentioned issues.
I’d assumed the border gate in question would be closed, so I’d planned to ask Aub Dunkelfelger to place teleporters between his country gate and the border gate he shared with Ahrensbach. - P5V8 (Their Information and Name Stones)
Geibe Kirnberger mentions the teleportation circles within each country gate, but I don't see any mention of those being connected to the Sovereignty.
“There’s no need to worry about that,” Giebe Kirnberger cackled. “To my knowledge, there are teleportation circles within each gate. They can be used only by Zents wielding the Grutrissheit.” - P5V4 (Kirnberger's Country Gate)