Did the father err by putting the puppy out on the street because it was unfit for guarding, and is the family complicit in this error, and what is its religious ruling, and how can atonement be made for it?

There is no sin upon your father for what he did; rather, his action was obligatory. This is based on the saying of the Prophet, peace and blessings be upon him: "Whoever keeps a dog, except a dog for herding livestock, hunting, or farming, his reward will be decreased by one qiraṭ each day." As long as the dog is not suitable for any of the purposes mentioned in the hadith, it is not permissible to keep it.