I would say that something with the morphological differences of a bulldog, for example, if it occurred in the wild, traditionally would have routinely been classified as a different genus from wolves. After all, Cape Hunting Dogs (Lycaon) and Dholes (Cuon) are classified as different genera from wolves, even though they resemble wolves far more than a bulldog (or many other breeds) do. (However, I don’t think the difference amounts to a familial one.)
Once you start talking about genetics you are getting into different territory. Many of the genetic differences between different forms are not due to selection, but are due to accumulation of random differences over time. These differences develop over thousands to millions of years, so there is no way you could create them in a short time without genetic engineering (that is, direct tinkering with the genome).
But you are confusing morphological and genetic similarity. Big changes in morphology can result from small genetic changes, while conversely, species can be very different genetically but very similar morphologically.
Years ago taxonomists had to rely purely on morphology, since genetic data was not available. New genetic data has in many cases caused a shift in taxonomy. Many species that were formerly classified in different genera on morphological grounds have now been merged in the same genus because they are not that different genetically.
One good example of this sort of thing is humans and chimps. Although quite distinct morphologically, humans and chimps are sufficiently alike genetically that there would be grounds for including them in the same genus. A Martian taxonomist might well do so. (And this is actually what Linneaus did, calling chimps Homo troglodytes).
As Gorsnak suggests, true family-level differences involve fairly radical morphological differences, and these could probably not be selected for in a coordinated way over a short period of time. Family-level genetic differences take tens of millions of years of evolution to accumulate.
However, I would point out that humans and chimps have traditionally been classified as different families on morphological grounds, even though genetically they could be in the same genus. It might be possible to select for a small number of regulatory genes that produced similar levels of morphological divergence in other animals.