Cirkus star Wolfgang Lauenburger (that is his name) with his "Dog-act" dogshow during privatshow (I think that is what this word means but am not 100 percent sure) in Verden 2010
very good translation mate, almost completely correct. ;)
the word "Privathengstshow" is no word you will find in a dictionary. it actually is a compound word, made of three words.
the best translation for the word would be, show for people with "privat" stallions. to make it easier, people show their stallions there. it is a show for "rding horses".
these compounds in the german language are sometimes strange as people, like in this case, create their own compounds.