The quarter panels are reaction injection molded (RIM) polyurethane. RIM is the process used to make the parts, not the material. In the case of the side panels, that material is a two-part polyurethane resin. Hence the name "reaction injection molding". You can't replicate the RIM process without extremely expensive mixing and injection-molding equipment, but you don't need to since you're just bonding the parts.
Unfortunately, it's pretty hard to bond with because you can't make new polymer chains with the base material of either piece as polyurethane is pretty much inert. You can't melt it together like a thermoplastic elastomer. The key properties for the adhesive will be flexibility and a similar coefficient of expansion. The correct surface preparation (surface roughness) on both parts will also help with the adhesion. If you look for an adhesive intended for flexible urethane bumper repair, that would probably be a good start.
[This message has been edited by Steven Snyder (edited 03-09-2015).]