If Serbia was a UN member state and Kosovo was apart of it, they would've have to sign kosovo away or else its a violation to their territorial integrity or else it wouldn't be legal according to international law. It has to happen internally if a country has international recognition like south Sudan did with North Sudan or eritrea did with Ethiopia and Kosovo would've been the same.
Go read the legal arguments around why Kosovo was recognized. They hinge on UNSC resolution 1244 which forced Yugoslavia forces out (the second Yugoslavia) and allowed for civilian adminstration of Kosovo indefinitely pending a final political settlement. At the end of the process Kosovo declared independence unilateraly and some countries recognized it. Serbia doesn't recognize it to this day.
That resolution 1244 ofcourse recognizes the sovereignty, territoritial integrity and unity of Yugoslavia (the second one).
Serbia went to the ICJ to ask if Kosovo's unilateral declaration of independence was against international law and the ICJ declared it was not. There's a lot of interesting aspects to the Kosovo situation.