it is always a sight (awkward) when dogs mate and the fact is there is no defined time until when the dogs would remain in that awkward position. However, this intertwining is not threatening to both dogs.
Here are the reasons why they get stuck:
The male Dogs has an organ known as Bulbus glandis, which is the major organ responsible for keeping dogs tied up together to the female dog. During this process, the semen being injected to the female dog will be well secured inside. This organ is known to expand and then gets locked in the uterus, and this gives the female dog higher chances of getting puppies cos When the male ejaculates, the knot swells enough to seal the vagina entirely, so no semen escapes. This position could last for 5 to 5 minutes or even as long as half an hour depending on several factors. However, it should be noted that the calmer the dog stays, the faster they get over it as disrupting or disturbing them during this moment could get them panic and will therefore induced anxiety making the locking position last longer.
But ideally, this tie shouldn’t last for 20 minutes and this depends on how the male dog will ejaculate his sperm into the female dog and once after this they get stuck until the bulbous glandis is back to its original size.
It is not uncommon for the male to dismount and turn around the opposite direction trying to pull away. Thats why they seem to be stuck butt-to-butt.
So, next time you gods at such position, kindly let them be