OK, so it starts.
1) I'm not a Washington lawyer, so I don't know the laws in that state compared to others. But, I can tell you that statutes in each state are more specific than "make you whole". While that is a figure of speach, the statute will generally say something like " The difference between fair market value before and after the accident" and will go on to qualify how fair market value, or that difference is determined, whether by the actual cost of repair or pre-accident value less salvage value. They do not owe to pay you what YOU think your car is worth.
2) Commercial Liability insurance is different than a personal auto policy. They,in some cases,may have a liability deductible just like you have on your own policy for your collision cover..except Hagerty does not have a deductible. Reporting a claim on their policy will almost automatically cause them to get a rate increase. They probably feel it is more economical to pay for your damage than have the rate increase. I agree this is a little self serving to them and they may change their mind when the estimates roll in. I agree, do not dilly dally around with them too much if at all. The police report will list their insurance company and you can also contact them yourself if they refuse to contact them. So, get a copy of the police report...hopefully one was made!
3) If you have the same Hagery policy I have, it is a Agreed Value Policy. Basically you told them what you thought your car was worth and they agreed to insure it UP TO that value. The policy will pay for repairs up to the agreed value. If you are a novice at insurance claims, you may want to contact Hagerty first. They can handle it for you, then subrogate for the money back from the other company, as Dan stated. However, if you choose to "go it alone" you will find yourself negotiating either the repair cost or value of the vehicle. The value of these cars is not cast in stone and each one is different. So do your research and be realistic. Another figure of speach is "they owe to put you back in the condition you were in before the loss". Again the statutes spell out exactly how that is determine in each state. If your car has NEVER been wrecked they could... potentially... owe you for the decrease in value, after repairs, due to deminished value.
4) Don't get in a rush. Take your time to make sure what you agree to is the correct decision for you. I'd start by getting a few reputable shops to look at your car and give an estimate to make sure it is even repairable within the value. Also do some research on value. I'm sure you have a pretty good idea what you think your car is worth. They won't pay $6000 to repair a $4500 car. I have no knowledge of your car, so I'm just throwing figures out. The important thing is that you feel you came out OK in the end.
It sounds as though you were not injured, which is a good thing...or you're just worried more about the car than yourself! If you have other "normal" cars that aren't insured through Hagerty, your agent may be able to put you on to some reputable shops in your area. Good luck and keep us posted on how it's going.