Do you have the legal definition for "authorized animals" as noted above, like is there a specific list? This sounds like housing for larger livestock (i.e. goats/pigs up to horses/cows) and not necessarily for smaller livestock, such a poultry, rabbits, etc.
If this is meant to include ANY livestock including poultry then that's really rough, a 50' setback requirement is nearly impossible to get on most in-city lots unless you have acreage to work with.
Re: front yards. Very rarely are animals allowed to be housed in a "front yard" unless you're in a rural/agricultural area. I technically have no backyard (on 4 acres, but "backyard" is no bigger than an average suburban one) so all animals, outbuildings, etc. go in my front yard. But I'm exempt from any city ordinances.