Q: "I need to attach polyethylene to another type of material such as wood-plastic-metal of various types. Any ideas?"
A: Polyethylene is a polyolefin and very difficult to achieve strong adhesion to. A common method to overcome this issue is to pre-treat the surface via corona discharge, gas plasma, flame treatment, or priming. These methods typically increase the surface energy of the substrate and the potential to adhere to it. Utilizing any of these pre-treatment methods will open up the choice of possible adhesive products. To bond surface-treated polyethylene to wood, plastic, or metal you can use a cyanoacrylate, epoxy, or polyurethane.
The right adhesive choice for you is not only dependent on the dimension, design, and substrates you are trying to assemble, but also the environment the device/item is being subjected to. Is it being used indoors with no contact to moisture or outdoors with consistent contact to water? For a dry environment, a cyanoacrylate might be the right choice, whereas an epoxy might be better for a moist environment.