You may have to add some support rods between the pieces other wise it may just break again ( as it will be the weakest point and thing always break at their weakest points )
super glue will be faster when bonding, but I find its brittle, two part epoxies are slower but are slightly more forgiving under strain. Only down side to epoxy over super glue is its thicker whereas super can almost hide the break
The plastic weld is a great idea. I would definitely use a support rod when gluing these pieces back together in the thick areas. Get yourself an 1/8" or 3/16" rod from home depot or lowes. Anything bigger than that wont flex well if your holes arent perfect. drill your holes, fill them with adhesive and put your rod in one side. Let it set and repeat the process in the other, spreading adhesive anywhere you can. E6000 might be good as it has a little flex. For the thin areas, use a 5 second fast set superglue or plastic welder. All of this stuff you can get at HD or lowes.