Probably best to start a new side.. but just for discussion reasons I can tell you what might work to fix it if you were wanting to.
Lay both parts down and butt glue it with epoxy.. try to keep the glue to a minimum. EVERYTHING STRAIGHT AND FLAT
Once it was dry .. I would take a thin dremel cutting wheel and cut a slice along the dowel and across the butt joint .. from the top to the bottom thru the center of the dowel.. Just an inch , inch and a half long.
Then I would get a good 1/16th to 3/32nd piece of aircraft ply and epoxy glue it in the slot.. outer grainon the ply running the same direction as the dowel.
After that dried, I would lay the fuse side flat, and sand a flat section on both sides across the butt joint. Sand it almost 1/8th deep...Make it over lap the butt joint about 1.5 inch each side.
Then I would again laminate ply wood on the outer sides of the joint.
Once you shape this wood back to being rounded you should have a true strong lamination that will be stronger than new dowel.