So just where did canines and cats diverge? Besides, they have a different number of chromosomes.
Dogs have 78 chromosomes, far more than humans and more than any other diploid organism. The massive increase in information in the dog genome is due to the mechanism of selection, artificially accelerated by man**. Without the selection by man, the differences between the genomes of cats and dogs would be far less.
**Note the importance is in the mechanism and not the 'who' of the selecting, any selection at all whether natural, sexual, kin, or human selection would accomplish the same changes, albeit at different speeds and possibly in a different direction. If the dog species were in the wild they would be considered a 'ring-species'.
Long time ago; the canids diverged from the rest of the Carnivora 50 - 60 MY ago. Wolves, dogs and coyotes are all interfertile; there are reports of dog/jackal hybrids; a few unconfirmed reports of hybrids with other canids, and none with other non-canid carnivores.