Painting cabinets - what about brown trim / bead / welt

Bin shellac base white primer will stick to plastic, glass, and practically anything else. Many years ago I primed some PVC pipe with it and then put on a finish coat of ordinary latex paint. Those PVC pipes have stood in my garden as low-voltage lamp posts for all these years and still look good!

I think Bin shellac would work on your plastic base molding. If the composition of the "fake wood" is unknown it might be a good idea to prime it with Bin also.

Good luck and happy camping.