My question involves an injury that occurred in the state of: Hawaii

What is the name of your state (only U.S. law)? Hawaii
My question is about an accident where a pedestrian (my wife) was hit by a car. The driver's insurance company paid $10,000 of her medical bills. That was the maximum for medical on the driver's insurance. The remainder of her medical bills (over $20,000) was paid by our medical insurance.

I am trying to settle with the driver's insurer on the liability portion of the insurance in compensation for pain & suffering. My medical insurer wants reimbursement for what they paid. They feel that the driver's insurance should pay & they have turned to a collection company to get that reimbursement.

The woman at collection agency told me that there are 2 separate liens or claims. They have a claim with the driver's insurer for reimbursement & I have a claim with the driver's insurer for pain & suffering. The woman from the driver's car insurer on the other hand told me that told me that she isn't going to pay the collection agency anything unless I tell her to. She is only dealing with me. If I want her to send my money directly to the collection agency, she will. Otherwise, she'll send it to me & it's up to me to deal with the collection agency, either paying them, or negotiating with them.

My feelings on this are that if my wife had been hospitalized because of an illness or because of an accident at home, our medical would have paid the bills & would not have expected us to repay them. That would be absurd. Why have them if that was the case? We might as well pay our medical bills directly if that was so. The only difference in this case, the only reason our medical insurer expects reimbursement is because another insurer is involved & they think that insurer should be the one to pay.

So, I believe that their quarrel is with the driver's insurer, not me & my wife. They should not expect to get reimbursement from us. Any money we receive from the driver's insurer is ours for the pain & suffering (plus she still needs further treatment), it's not for reimbursing the medical insurer. Even the woman from the collection company told me that our claim with the car insurer & their claim with the car insurer are two different claims. If that is so, then they should be going after the driver's insurer & not be coming after us for their money. Yet it seems like that is what they intend to do, come after us.

Sorry it's so long, but my questions are:
1. Am I legally bound to reimburse the medical insurer, or is their fight with the driver's insurer? If I'm required to reimburse them, why? The only reason they expect their money back is because another insurer is involved. If they weren't in the picture, there wouldn't be this issue.

2. If I attempt to reach a settlement before the statute of limitations runs out but this arguing about who should pay takes us past the deadline, can I still collect our claim when everything is ironed out?

Thank you.