Hi fish,
that hose goes to a container under the fender. It's supposed to catch coolant, that in case of temp>120/140 C makes it's way pass the seal of the radiator cap. In return the same hose will suck the coolant back into the system, out of the bottle, when it cools down. That's what is alowed by suction valve in the center of the radiator cap.
Repair the hose properly and change your radiator cap. If your car is not overheating, it's actual compression pressure causing this problem. Then you'll have to bite the bullet and get the head job done with.
All the best,
Dokta