will a hot glue gun hold plastic together?
It depends on the type of plastic. Try superglue ( cyanoacrylate)- if that doesn't work try modeling cement. If that fails, try epoxy. I would not recommend hot glue, since it will likely distort the plastic.
You really need to identify what type of plastic it is first. Hot glue wouldn't be my first choice. A super glue of some sort would be better. Or an epoxy. You need something that fuses the plastic together.
Any adhesive will cost you eight bucks and will not work. The only way to repair some plastics- for example, ABS or PVC, is to use a solvent based glue which actually melts the plastic and welds it back together. The strength of the weld made is proportional to the amount of surface area glued. In this trapeze handle, there is not enough surface area to withstand the weight of a small child, let alone the forces which will be exerted upon the handle. That said, according to your link, you can buy a new set of handles for twelve dollars. Why not do that? You'll have a back up, and you won't have any broken boned children.
There are many types of plastic - some melt with heat, some burn (not at hot melt glue temps) Some are welded with solvents and some shed solvents Although it doesn't work on all plastics, GOOP Craft is a clear silicone adhesive that sets hard and can be used as a soft squishy glue that must be supported while it sets or can be used as a contact cement - pull it apart, hold about 10-15 seconds, replace and you can't easily move it. If it doesn't work, you can peel it off.
