With the damaged ship not being able to jump the yardship either needs to fix the damaged ship or scuttle it? Could they drop the KF drive and bring whats left of the ship to the home port?
This is exactly what they will have to do. They take off the salvageable components, then put a beacon on the KF core. The yardship brings the salvage back, and another vessel later delivers civilian Dropships to rubble the KF core so it won't interfere with KF formation. The KF rubble is transported via Dropship cargo bays to a facility that makes new KF cores, and used as raw materials.
If the Yardship is able to fix the KF core, it will still take as much of the salvage on board itself as possible, then put a small computer on the KF core. The Yardship provides the charging power to the KF core and coordinates to the computer. The KF core jumps first, and the Yardship follows. Repeat until the KF core is at a shipyard.
The reason the Yardship might choose not to repair the core is KF core vessels are expensive investments, and you want to keep them working on stuff in their price range. If the KF core is badly damaged enough, dropping off Dropships is the cheaper route (since you are using civilian KF cores briefly, instead of a compact KF core for an extended time frame). From there is a fancier version of people with sledgehammers breaking rocks, in terms of rubbling the KF core.
This all assumes the Yardship can jump the vessel to a proper shipyard. If you are salvaging a Warship you might have to leave the Yardship on site because there is nowhere to go. The Yardship itself might only be to deliver a space station (with repair yard) to the location, and the space station itself handles repairs. If you don't even have the repair station, you are stuck with the Yardship on site for months performing the repairs/replacement needed.
Now I'm starting to get more respect for Comstar/WoB as they were snagging Warships during the Succession Wars. They were busy and frustrated, working on a project that they might never see the result of in their lifetime.