I generally don't try to reconcile the idea of objective morality - it has too many contradictions, and is not a useful model, IMO.
Epistemic status: amateur, personal intuitions.
If this were the case, it makes sense to hold dogs (rather than their owners, or their breeding) responsible for aggressive or violent behaviour.
I'd consider whether punishing the dog would make the world better, or whether changing the system that led to its breeding, or providing incentives to the owner or any combination of other actions would be most effective.
Consequentialism is about considering the consequences of actions to judge them, but various people might wield this in various ways.
Implicitly, with this concept of responsibility, you're considering a deontological approach to bad behavior: punish the guilty (perhaps using consequentialism to determine who's guilty though that's unclear from your argumentation afaict).
In an idealized case, I care about whether the environment I evolve in (including other people's and other people's dogs' actions) is performing well only insofar as I can change it, or said otherwise, I care only about how I can perform better.
(Then, because the world is messy, and I need to account for coordination with other people whose intuitions might not match mine, and society's recommendations, and my own human impulses etc... My moral system is only an intuition pump for lack of satisfactory metaethics.)
[...]only autonomous (driven by internal will) actions, derived from duty to the moral law, can be considered moral.
[...] a belief in a thing has a totalising effect on the will of the subject.
What makes this totalizing effect distinct from the "duty to moral law" explicitly called for?
A slave is ordered to kill by his master. As the slave is deprived of his autonomy, it seems intuitive that the master is morally responsible for this action, not the slave. This argument is derived (in spirit) from Immanuel Kant, who argued that only autonomous (driven by internal will) actions, derived from duty to the moral law, can be considered moral. Duty, in turn, is derived from rational deliberation. Kant contrasts autonomous actions with heteronomous actions, which are driven by external will.
(I know that paragraph sounds very AI-generated but I promise it is not.)
An extension of this line of thinking can be made. A religious person commits actions due to their belief in an all-powerful thing. I use the word thing rather than God because it allows generalisation to non-Western conceptions of religion. In Abrahamic religions, this thing may be God, in Dharmic religions, it may be a belief in karma, samsara, dharma, etc.
A religious person's actions are, in a sense, heteronomous, as they are derived from the will of the thing.
What is interesting to me is that this thing doesn't have to exist - instead, the belief in the thing is sufficient. If one believes in an external thing, to any meaningful extent, their actions are influenced by it, and as such, are heteronomous and not liable to moral judgment.
Just as the master has a totalising control over the will of the slave, a belief in a thing has a totalising effect on the will of the subject.
Now, following from this argument, this thing is not limited to traditional religion. Instead it may be modified to the concept of an objective morality.
This would make the idea of an objective morality self-defeating. If it exists, it has a monopoly on the will of individuals, and as such, actions are heteronomous and not subject to moral judgments. If it doesn't exist, and an individual believes in it, it has the same totalising effect on will. The only case in which an action is moral is if objective morality, does not, in fact, exist (or the individual does not believe in it), and instead the individual does it out of his own autonomous will.
An obvious objection to this is simple: humans famously do not act solely out of rational, free will but often out of impulse, or desire. If we accept that these capricious actions are subject to moral judgments, then we have no reason not to morally prosecute a dog (rather than its owner) who, because of its breeding or environment, cannot help but be aggressive. The rebuttal, to me, seems straightforward. A unique property of will is its ability to supersede desire or impulse. The dog, unlike the human, does not have will and as such cannot override its desires. The will of the human is able to override a desire or impulse. As such, a human can be held liable in a way that a dog cannot.
This whole line of inquiry, however, is based in the deontological arguments of Kant. Consequentialists argue that the outcome of an action is paramount in determining its moral worth. This seems paradoxical to me, however. The consequentialist would be implicitly arguing that will is not necessary for moral behaviour. If this were the case, it makes sense to hold dogs (rather than their owners, or their breeding) responsible for aggressive or violent behaviour. It would also suggest that the mountain should take moral responsibility for the deaths caused by a landslide. If the consequences of an action are the key metric for moral worth, why stop at humans? The consequentialist would have to provide a reason that humans are uniquely qualified to bear moral responsibility that does not invoke will. Intelligence is the knee-jerk substitution, however, an ability to use rationality is moot if not combined with a will to commit behaviour.
How do you reconcile the idea of objective morality with the free will of an individual?