I would get a knife/flathead screwdriver into the crack to wedge it open slightly, then get the pva into the gap, I use a syringe but it isn't necessary to do so, I just find it easier. (Printers ink needles are cheap on eBay and work brilliantly)
Sellotape or use a clamp to hold the crack closed for a few hours (use some wedges of scrap wood or some folded cardboard to protect the willow from the clamp, try to spread the pressure of the clamp basically)
Remove everything and sand to a neat finish, done.