Queen Elizabeth II is well known as an affectionate breeder of Welsh Pembroke Corgi dogs; most of the pups she keeps from litters born to her dogs are female. Her sister Princess Margaret had a male Miniature Long-Haired Dachshund called Pipkin who seemed to love the Corgis in quite a different way from their owner -- a litter of seven Dachsund/Corgi crosses was born to one of the Queen's dogs. However, Elizabeth found them appealing enough to christen the type "Dorgi" and arrange for more to be born. (This is occasionally spelled "Dorgie".)
Photographer Norman Parkinson was apparently bold enough to ask how the short-legged Miniature Dachshund could manage to mate with the comparatively taller Corgi and was told by the Queen, "Oh, it's quite simple. We have a little brick."
The Secretary of the Kennel Club at the time of the portrait conflict is supposed to have remarked, "The Dachshund was evolved to chase badgers down holes and Corgis to round up cattle. If anyone loses a herd of cattle down a badger hole, these are just the dogs to get them out."