What do I have?

Old bit of Chinese wisdom- if you want to know the true value of something you own, get the opinion of three non-related men who have no interest in buying it. Mr. Chaddick is a very well established gun dealer in Terrel, TX and has a good reputation, as does Jack Puglisi, Steven Cobb and other too numerous to mention here. However, I would also discuss this situation with Jess Brliley and also with Danny Clark of Collectors Firearms- both are in the Houston area. Mr. Chaddick is 100% correct in that the CH(E) guns are scarce, and the smaller sized frames and gauges may well be one reason for the value of your family Parker. The DH(E) or grade 3 numerically was not all that much different in engraving or stock checkering than the more costly CH(E), and was a bit like the fabled "red-headed stepchild" between the very popular DH(E) and the grade 5 BHE Parker, so there were not all that many manufactured. The late Ed Muderlak points this out in his book on the Parker- The Old Reliable and has some fine details about his visits and chats with Herschel Chaddick in past years. If you haven't yet read his writings, you might like to do so. And you are 100% correct about Bruce Day- if he makes a recommendation to you about guns and gunning, his advice is as solid as the Rock of Gibraltar!