Your wheel barrow repair job is not unlike what a poly kayak owner may be faced with. The most common method of sealing separated seams or open cracks, is by heat-welding. It's done with a propane torch and poly "rods" to match the damaged material - similar to metal welding.

Scroll down to the bottom of the page at the link below to learn more about this.

Here is a link that might be useful: Heat welding Polyethylene

There is another alternative. Poly-Weld Adhesive from TAP. Finally an adhesive for polyethylene plastics. It requires a minor procedure called flame treating which is essentially just whisking the plastic to be repaired with a propane torch to prep the surface. I'd like to hear some reviews from guys who have used it

Here is a link that might be useful: Poly-Weld Adhesive fromTAP

bertman, your idea about screen is one that I would probably try, along with a good epoxy. However, I would use hardware cloth rather than plastic screening. Smallest hole hardware cloth you can find, perhaps 3" by 10," in a bed of epoxy and another coat of epoxy over the top of the cloth. You may need to pre-form the hardware cloth so that it fits the surface. And I would do it on the top and bottom of the tray.

Epoxy will fail on polyethylene in 5 minutes.

Here is a video showing the application of Mr Stickeys glue for poly.

Here is a link that might be useful: metacafe.com

I cut a piece of 3/4" plywood and sandwiched it between the frame and bucket. Wish I had thought of this before I threw in the fire log.