[Arran]

Bob;
Now that you have the veneer stripped off it more obvious what the point of failure was, the laid the walnut veneer directly over that piece of oak or ash quarter round molding. The set was obviously stored in a damp place, judging by the condition of the finish, the chassis rust, and the failed glue joints, so that piece of 1/4 round likely swelled up cracking the veneer across the grain. The typical practice was to place a layer of veneer under the finished layer, with the grain running in the opposite direction, rather like in plywood, which would make it more stable, in fact the best way would be to use five layers, it looks like they only used three here.
Regards
Arran