For some reason we keep covering the same ground, you and I.

I don't know why you seem to want our case be a certain way, but it just isn't how you describe.
I don't think it is unusual at all to involve our insurance at any stage. Our agent has been informed from the beginning and told us to call him if there were any problems. Why would he do that if it is so cut and dry as you describe? He didn't tell us we won't work with you if you work with the other company. Where do you get this information of yours??
I couldn't foresee any trouble with the other party's insurance. But our agent did say he would speak to their agent if we needed him to. He offered. I declined because the other party's insurance is still working with us. We haven't had any problems yet. We discussed it and he did see it could get even more complicated. Then our agent told us, "good luck", in dealing with the other insurance agency as it is already a complicated matter. It wasn't shutting the door for us to use ours. For some reason this is a sticking point with you. I don't understand why.
I do understand that you don't know what we expect from our insurance company. I expect guidance and maneuvering with the other insurance company to get us to the point where the vehicle is reliable
or if it cannot be repaired to be compensated in some amount to get a "like" vehicle.
Not new. We can not accept a vehicle that is not reliable. And we still need a vehicle.
Additionally, selling the vehicle would not bring much. Now it has a history of being in an accident, extensive damage, and it isn't reliable. Not much of a market for that.
Anyway, it isn't helpful to keep going back and forth about the insurance. It isn't an issue. But for some reason you keep wanting to point out it is. Even when I tell you it is not.

Why is that?
ETA- Once we file a claim with our insurance, I imagine they would take over where the gaps are and would pursue the other party's insurance to be reimbursed by them.