Polycarbonate is very sensitive to chemicals. Most polycarbonate parts are painted or "hard coated" like automotive headlights. You have to even be careful with the paint - solvents swell into polycarbonate, cause the plastic to crack, then the solvent evaporates out to leave an ugly bond. Be careful of the adhesives you use. Polyurethane adhesives tend to work well - especially 2k polyurethanes but check the adhesive manufacturers recommendation.
For acrylic, there are "solvent free" or foam safe epoxies that will not cause hazing on acrylics.