First, cork is a wonderful floor. I am an architect. I push it on every project I have (not always with success). I have had it in two houses.
The vendor of the best cork flooring that I know of is Dodge-Regupol (www.regupol.com)
. Theirs is 12x12 glue-down. The best installation is to lay unfinished tile, then to finish with polyurethane. Waxed cork feels nicer to bare feet, but requires more maintenance (annual waxing and buffing). This is institutional grade cork: the type that lasts 60 to 100 years with proper maintenance.
I strongly recommend against the fancy cork patterns: you are getting a thin veneer over a low quality cork back. Because cork is relatively soft, it's also easily cut by dropped knives and other sharp objects. The Regupol cork absorbs this type of damage gracefully, but I don't think this type will. It is also un-refinishable because the surface you bought to look at is so thin.
Poor adhesion and adhesive failure is probably a function of moisture. If your trailer leaks at all, or if there is any
moisture in the subfloor, you will have a problem. This is true for all types of glued-down flooring. Newer formulations of adhesives are much more moisture-sensitive than older adhesives (formulations changed to comply with air quality standards). If you can get hold of "cut back adhesive" it should be less of a problem.
Because of moisture issues, a floating floor might be a good compromise.
Re dogs: the only floors that will stand up to 120 lb. dogs with no damage are concrete, ceramic tile, and steel plate. I have rambunctious 70 lb. dogs, and they scratch the polyurethane, but the cork itself is unharmed. Also 4 boys. I'd do cork again in a heartbeat.