It's the Bulbis Glandis... the part of the male dog's apparatus... When mating with the female, a corresponding muscular ring in her receiving organ grips the bulb and results in what breeders call a tie. It's an adaptation to assure the mating male dog father's the litter of a female in estrus. The tie can last several minutes or more following mating, resulting in the genre' of humor (humour?) concerning two black dogs...
(The euphemisms are necessary since the value's of the censorial 'bots are undetermined)...
By the way, on a semi-serious note, you need to break the dog of this habit... remove the teddy and discipline him in an appropriate manner...