I can’t say for sure this doesn’t vary by state, but generally, you would file against the person who hit you. You have no contract with Arbella; Arbella has a contract with the person who hit you to indemnify them against liability arising from their operation of a vehicle.
Since this is a third-party liability claim, my understanding is that the insurer is only really obligated to pay you anything if a court rules as such (i.e. a judgment against their insured). The confusion is that, from your perspective, your insurer has filed a claim (subrogation) with Arbella and already had your repairs paid for. That, to my understanding, is basically the same as a pre-litigation settlement – the insurer reviews the case and determines their insured would likely be found liable by a court for the loss (if the case proceeded to litigation). Maybe they could take a hardline stance and say “we don’t settle claims; get a judgment against our insured and then we’ll pay for your repairs” (although this sounds like bad faith), but they have an obligation to defend their insured (which means paying for legal fees), and they know it would be foolish to pay legal fees to defend against a case they’ve determined they’re likely to lose.
It sounds like Arbella agrees that their insured was likely at fault for the collision, and they agree that their insured (and by extension, them as the insurer) is likely liable for the vehicle repairs, which is why they’ve paid those already without litigation. The disagreement (or more realistically, from what I hear, bad-faith blanket denial) is over whether their insured is liable for diminished value, and how much. As with any other legal dispute, if you can’t come to an agreement on your own, only a court can force the other party to do something. (Simplified, and assuming there is no arbitration agreement in play.)